sudoku9([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]). clause(1, sudoku9(var('Rows')), (var('Rows') = [[1, anonymous(1), anonymous(2), anonymous(3), anonymous(4), 7, anonymous(5), 9, anonymous(6)], [anonymous(7), 3, anonymous(8), anonymous(9), 2, anonymous(10), anonymous(11), anonymous(12), 8], [anonymous(13), anonymous(14), 9, 6, anonymous(15), anonymous(16), 5, anonymous(17), anonymous(18)], [anonymous(19), anonymous(20), 5, 3, anonymous(21), anonymous(22), 9, anonymous(23), anonymous(24)], [anonymous(25), 1, anonymous(26), anonymous(27), 8, anonymous(28), anonymous(29), anonymous(30), 2], [6, anonymous(31), anonymous(32), anonymous(33), anonymous(34), 4, anonymous(35), anonymous(36), anonymous(37)], [3, anonymous(38), anonymous(39), anonymous(40), anonymous(41), anonymous(42), anonymous(43), 1, anonymous(44)], [anonymous(45), 4, anonymous(46), anonymous(47), anonymous(48), anonymous(49), anonymous(50), anonymous(51), 7], [anonymous(52), anonymous(53), 7, anonymous(54), anonymous(55), anonymous(56), 3, anonymous(57), anonymous(58)]], sudoku9_rows(var('Rows')), sudoku9_transpose(var('Rows'), var('Columns')), sudoku9_rows_distinct(var('Columns')), sudoku9_blocks(var('Rows')), sudoku9_flatten(var('Rows'), var('Cells')), labeling([ff], var('Cells')))). clause(2, sudoku9_rows([]), true). clause(3, sudoku9_rows([var('Row') | var('Rows')]), (var('Row') ins 1..9, all_distinct(var('Row')), sudoku9_rows(var('Rows')))). clause(4, sudoku9_rows_distinct([]), true). clause(5, sudoku9_rows_distinct([var('Row') | var('Rows')]), (all_distinct(var('Row')), sudoku9_rows_distinct(var('Rows')))). clause(6, sudoku9_transpose([[] | anonymous(1)], []), true). clause(7, sudoku9_transpose(var('Rows'), [var('Column') | var('Columns')]), (sudoku9_heads_tails(var('Rows'), var('Column'), var('Tails')), sudoku9_transpose(var('Tails'), var('Columns')))). clause(8, sudoku9_heads_tails([], [], []), true). clause(9, sudoku9_heads_tails([[var('Head') | var('Tail')] | var('Rows')], [var('Head') | var('Heads')], [var('Tail') | var('Tails')]), sudoku9_heads_tails(var('Rows'), var('Heads'), var('Tails'))). clause(10, sudoku9_blocks([]), true). clause(11, sudoku9_blocks([var('A'), var('B'), var('C') | var('Rows')]), (sudoku9_block_row(var('A'), var('B'), var('C')), sudoku9_blocks(var('Rows')))). clause(12, sudoku9_block_row([], [], []), true). clause(13, sudoku9_block_row([var('A'), var('B'), var('C') | var('As')], [var('D'), var('E'), var('F') | var('Bs')], [var('G'), var('H'), var('I') | var('Cs')]), (all_distinct([var('A'), var('B'), var('C'), var('D'), var('E'), var('F'), var('G'), var('H'), var('I')]), sudoku9_block_row(var('As'), var('Bs'), var('Cs')))). clause(14, sudoku9_flatten([], []), true). clause(15, sudoku9_flatten([var('Row') | var('Rows')], var('Cells')), (sudoku9_append(var('Row'), var('Rest'), var('Cells')), sudoku9_flatten(var('Rows'), var('Rest')))). clause(16, sudoku9_append([], var('Ys'), var('Ys')), true). clause(17, sudoku9_append([var('X') | var('Xs')], var('Ys'), [var('X') | var('Zs')]), sudoku9_append(var('Xs'), var('Ys'), var('Zs'))). step(sudoku9([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(1), ['Rows' = [[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Columns' = [[1, 5, 7, 4, 9, 6, 3, 2, 8], [6, 3, 8, 7, 1, 2, 5, 4, 9], [2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]], 'Cells' = [1, 6, 2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [[[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]] = [[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], sudoku9_rows([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), sudoku9_transpose([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [[1, 5, 7, 4, 9, 6, 3, 2, 8], [6, 3, 8, 7, 1, 2, 5, 4, 9], [2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), sudoku9_rows_distinct([[1, 5, 7, 4, 9, 6, 3, 2, 8], [6, 3, 8, 7, 1, 2, 5, 4, 9], [2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), sudoku9_blocks([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), sudoku9_flatten([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [1, 6, 2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), labeling([ff], [1, 6, 2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]] = [[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], builtin, [], []). step(sudoku9_rows([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(3), ['Row' = [1, 6, 2, 8, 5, 7, 4, 9, 3], 'Rows' = [[5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]], [[1, 6, 2, 8, 5, 7, 4, 9, 3] ins 1..9, all_distinct([1, 6, 2, 8, 5, 7, 4, 9, 3]), sudoku9_rows([[5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]])]). step([1, 6, 2, 8, 5, 7, 4, 9, 3] ins 1..9, builtin, [], []). step(all_distinct([1, 6, 2, 8, 5, 7, 4, 9, 3]), builtin, [], []). step(sudoku9_rows([[5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(3), ['Row' = [5, 3, 4, 1, 2, 9, 6, 7, 8], 'Rows' = [[7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]], [[5, 3, 4, 1, 2, 9, 6, 7, 8] ins 1..9, all_distinct([5, 3, 4, 1, 2, 9, 6, 7, 8]), sudoku9_rows([[7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]])]). step([5, 3, 4, 1, 2, 9, 6, 7, 8] ins 1..9, builtin, [], []). step(all_distinct([5, 3, 4, 1, 2, 9, 6, 7, 8]), builtin, [], []). step(sudoku9_rows([[7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(3), ['Row' = [7, 8, 9, 6, 4, 3, 5, 2, 1], 'Rows' = [[4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]], [[7, 8, 9, 6, 4, 3, 5, 2, 1] ins 1..9, all_distinct([7, 8, 9, 6, 4, 3, 5, 2, 1]), sudoku9_rows([[4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]])]). step([7, 8, 9, 6, 4, 3, 5, 2, 1] ins 1..9, builtin, [], []). step(all_distinct([7, 8, 9, 6, 4, 3, 5, 2, 1]), builtin, [], []). step(sudoku9_rows([[4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(3), ['Row' = [4, 7, 5, 3, 1, 2, 9, 8, 6], 'Rows' = [[9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]], [[4, 7, 5, 3, 1, 2, 9, 8, 6] ins 1..9, all_distinct([4, 7, 5, 3, 1, 2, 9, 8, 6]), sudoku9_rows([[9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]])]). step([4, 7, 5, 3, 1, 2, 9, 8, 6] ins 1..9, builtin, [], []). step(all_distinct([4, 7, 5, 3, 1, 2, 9, 8, 6]), builtin, [], []). step(sudoku9_rows([[9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(3), ['Row' = [9, 1, 3, 5, 8, 6, 7, 4, 2], 'Rows' = [[6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]], [[9, 1, 3, 5, 8, 6, 7, 4, 2] ins 1..9, all_distinct([9, 1, 3, 5, 8, 6, 7, 4, 2]), sudoku9_rows([[6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]])]). step([9, 1, 3, 5, 8, 6, 7, 4, 2] ins 1..9, builtin, [], []). step(all_distinct([9, 1, 3, 5, 8, 6, 7, 4, 2]), builtin, [], []). step(sudoku9_rows([[6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(3), ['Row' = [6, 2, 8, 7, 9, 4, 1, 3, 5], 'Rows' = [[3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]], [[6, 2, 8, 7, 9, 4, 1, 3, 5] ins 1..9, all_distinct([6, 2, 8, 7, 9, 4, 1, 3, 5]), sudoku9_rows([[3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]])]). step([6, 2, 8, 7, 9, 4, 1, 3, 5] ins 1..9, builtin, [], []). step(all_distinct([6, 2, 8, 7, 9, 4, 1, 3, 5]), builtin, [], []). step(sudoku9_rows([[3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(3), ['Row' = [3, 5, 6, 4, 7, 8, 2, 1, 9], 'Rows' = [[2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]], [[3, 5, 6, 4, 7, 8, 2, 1, 9] ins 1..9, all_distinct([3, 5, 6, 4, 7, 8, 2, 1, 9]), sudoku9_rows([[2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]])]). step([3, 5, 6, 4, 7, 8, 2, 1, 9] ins 1..9, builtin, [], []). step(all_distinct([3, 5, 6, 4, 7, 8, 2, 1, 9]), builtin, [], []). step(sudoku9_rows([[2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(3), ['Row' = [2, 4, 1, 9, 3, 5, 8, 6, 7], 'Rows' = [[8, 9, 7, 2, 6, 1, 3, 5, 4]]], [[2, 4, 1, 9, 3, 5, 8, 6, 7] ins 1..9, all_distinct([2, 4, 1, 9, 3, 5, 8, 6, 7]), sudoku9_rows([[8, 9, 7, 2, 6, 1, 3, 5, 4]])]). step([2, 4, 1, 9, 3, 5, 8, 6, 7] ins 1..9, builtin, [], []). step(all_distinct([2, 4, 1, 9, 3, 5, 8, 6, 7]), builtin, [], []). step(sudoku9_rows([[8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(3), ['Row' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Rows' = []], [[8, 9, 7, 2, 6, 1, 3, 5, 4] ins 1..9, all_distinct([8, 9, 7, 2, 6, 1, 3, 5, 4]), sudoku9_rows([])]). step([8, 9, 7, 2, 6, 1, 3, 5, 4] ins 1..9, builtin, [], []). step(all_distinct([8, 9, 7, 2, 6, 1, 3, 5, 4]), builtin, [], []). step(sudoku9_rows([]), fact(2), [], []). step(sudoku9_transpose([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [[1, 5, 7, 4, 9, 6, 3, 2, 8], [6, 3, 8, 7, 1, 2, 5, 4, 9], [2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(7), ['Rows' = [[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Column' = [1, 5, 7, 4, 9, 6, 3, 2, 8], 'Columns' = [[6, 3, 8, 7, 1, 2, 5, 4, 9], [2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]], 'Tails' = [[6, 2, 8, 5, 7, 4, 9, 3], [3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [1, 5, 7, 4, 9, 6, 3, 2, 8], [[6, 2, 8, 5, 7, 4, 9, 3], [3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]), sudoku9_transpose([[6, 2, 8, 5, 7, 4, 9, 3], [3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [[6, 3, 8, 7, 1, 2, 5, 4, 9], [2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(sudoku9_heads_tails([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [1, 5, 7, 4, 9, 6, 3, 2, 8], [[6, 2, 8, 5, 7, 4, 9, 3], [3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 1, 'Tail' = [6, 2, 8, 5, 7, 4, 9, 3], 'Rows' = [[5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [5, 7, 4, 9, 6, 3, 2, 8], 'Tails' = [[3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [5, 7, 4, 9, 6, 3, 2, 8], [[3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [5, 7, 4, 9, 6, 3, 2, 8], [[3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 5, 'Tail' = [3, 4, 1, 2, 9, 6, 7, 8], 'Rows' = [[7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [7, 4, 9, 6, 3, 2, 8], 'Tails' = [[8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [7, 4, 9, 6, 3, 2, 8], [[8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [7, 4, 9, 6, 3, 2, 8], [[8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 7, 'Tail' = [8, 9, 6, 4, 3, 5, 2, 1], 'Rows' = [[4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [4, 9, 6, 3, 2, 8], 'Tails' = [[7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [4, 9, 6, 3, 2, 8], [[7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [4, 9, 6, 3, 2, 8], [[7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 4, 'Tail' = [7, 5, 3, 1, 2, 9, 8, 6], 'Rows' = [[9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [9, 6, 3, 2, 8], 'Tails' = [[1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [9, 6, 3, 2, 8], [[1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [9, 6, 3, 2, 8], [[1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 9, 'Tail' = [1, 3, 5, 8, 6, 7, 4, 2], 'Rows' = [[6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [6, 3, 2, 8], 'Tails' = [[2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [6, 3, 2, 8], [[2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [6, 3, 2, 8], [[2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 6, 'Tail' = [2, 8, 7, 9, 4, 1, 3, 5], 'Rows' = [[3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [3, 2, 8], 'Tails' = [[5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [3, 2, 8], [[5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [3, 2, 8], [[5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 3, 'Tail' = [5, 6, 4, 7, 8, 2, 1, 9], 'Rows' = [[2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [2, 8], 'Tails' = [[4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [2, 8], [[4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [2, 8], [[4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 2, 'Tail' = [4, 1, 9, 3, 5, 8, 6, 7], 'Rows' = [[8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [8], 'Tails' = [[9, 7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[8, 9, 7, 2, 6, 1, 3, 5, 4]], [8], [[9, 7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[8, 9, 7, 2, 6, 1, 3, 5, 4]], [8], [[9, 7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 8, 'Tail' = [9, 7, 2, 6, 1, 3, 5, 4], 'Rows' = [], 'Heads' = [], 'Tails' = []], [sudoku9_heads_tails([], [], [])]). step(sudoku9_heads_tails([], [], []), fact(8), [], []). step(sudoku9_transpose([[6, 2, 8, 5, 7, 4, 9, 3], [3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [[6, 3, 8, 7, 1, 2, 5, 4, 9], [2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(7), ['Rows' = [[6, 2, 8, 5, 7, 4, 9, 3], [3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], 'Column' = [6, 3, 8, 7, 1, 2, 5, 4, 9], 'Columns' = [[2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]], 'Tails' = [[2, 8, 5, 7, 4, 9, 3], [4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[6, 2, 8, 5, 7, 4, 9, 3], [3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [6, 3, 8, 7, 1, 2, 5, 4, 9], [[2, 8, 5, 7, 4, 9, 3], [4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]), sudoku9_transpose([[2, 8, 5, 7, 4, 9, 3], [4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [[2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(sudoku9_heads_tails([[6, 2, 8, 5, 7, 4, 9, 3], [3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [6, 3, 8, 7, 1, 2, 5, 4, 9], [[2, 8, 5, 7, 4, 9, 3], [4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 6, 'Tail' = [2, 8, 5, 7, 4, 9, 3], 'Rows' = [[3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [3, 8, 7, 1, 2, 5, 4, 9], 'Tails' = [[4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [3, 8, 7, 1, 2, 5, 4, 9], [[4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[3, 4, 1, 2, 9, 6, 7, 8], [8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [3, 8, 7, 1, 2, 5, 4, 9], [[4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 3, 'Tail' = [4, 1, 2, 9, 6, 7, 8], 'Rows' = [[8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [8, 7, 1, 2, 5, 4, 9], 'Tails' = [[9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [8, 7, 1, 2, 5, 4, 9], [[9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[8, 9, 6, 4, 3, 5, 2, 1], [7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [8, 7, 1, 2, 5, 4, 9], [[9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 8, 'Tail' = [9, 6, 4, 3, 5, 2, 1], 'Rows' = [[7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [7, 1, 2, 5, 4, 9], 'Tails' = [[5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [7, 1, 2, 5, 4, 9], [[5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[7, 5, 3, 1, 2, 9, 8, 6], [1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [7, 1, 2, 5, 4, 9], [[5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 7, 'Tail' = [5, 3, 1, 2, 9, 8, 6], 'Rows' = [[1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [1, 2, 5, 4, 9], 'Tails' = [[3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [1, 2, 5, 4, 9], [[3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[1, 3, 5, 8, 6, 7, 4, 2], [2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [1, 2, 5, 4, 9], [[3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 1, 'Tail' = [3, 5, 8, 6, 7, 4, 2], 'Rows' = [[2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [2, 5, 4, 9], 'Tails' = [[8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [2, 5, 4, 9], [[8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[2, 8, 7, 9, 4, 1, 3, 5], [5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [2, 5, 4, 9], [[8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 2, 'Tail' = [8, 7, 9, 4, 1, 3, 5], 'Rows' = [[5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [5, 4, 9], 'Tails' = [[6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [5, 4, 9], [[6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[5, 6, 4, 7, 8, 2, 1, 9], [4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [5, 4, 9], [[6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 5, 'Tail' = [6, 4, 7, 8, 2, 1, 9], 'Rows' = [[4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [4, 9], 'Tails' = [[1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [4, 9], [[1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[4, 1, 9, 3, 5, 8, 6, 7], [9, 7, 2, 6, 1, 3, 5, 4]], [4, 9], [[1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 4, 'Tail' = [1, 9, 3, 5, 8, 6, 7], 'Rows' = [[9, 7, 2, 6, 1, 3, 5, 4]], 'Heads' = [9], 'Tails' = [[7, 2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[9, 7, 2, 6, 1, 3, 5, 4]], [9], [[7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[9, 7, 2, 6, 1, 3, 5, 4]], [9], [[7, 2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 9, 'Tail' = [7, 2, 6, 1, 3, 5, 4], 'Rows' = [], 'Heads' = [], 'Tails' = []], [sudoku9_heads_tails([], [], [])]). step(sudoku9_transpose([[2, 8, 5, 7, 4, 9, 3], [4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [[2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(7), ['Rows' = [[2, 8, 5, 7, 4, 9, 3], [4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], 'Column' = [2, 4, 9, 5, 3, 8, 6, 1, 7], 'Columns' = [[8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]], 'Tails' = [[8, 5, 7, 4, 9, 3], [1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[2, 8, 5, 7, 4, 9, 3], [4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [2, 4, 9, 5, 3, 8, 6, 1, 7], [[8, 5, 7, 4, 9, 3], [1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]), sudoku9_transpose([[8, 5, 7, 4, 9, 3], [1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [[8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(sudoku9_heads_tails([[2, 8, 5, 7, 4, 9, 3], [4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [2, 4, 9, 5, 3, 8, 6, 1, 7], [[8, 5, 7, 4, 9, 3], [1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 2, 'Tail' = [8, 5, 7, 4, 9, 3], 'Rows' = [[4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], 'Heads' = [4, 9, 5, 3, 8, 6, 1, 7], 'Tails' = [[1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [4, 9, 5, 3, 8, 6, 1, 7], [[1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[4, 1, 2, 9, 6, 7, 8], [9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [4, 9, 5, 3, 8, 6, 1, 7], [[1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 4, 'Tail' = [1, 2, 9, 6, 7, 8], 'Rows' = [[9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], 'Heads' = [9, 5, 3, 8, 6, 1, 7], 'Tails' = [[6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [9, 5, 3, 8, 6, 1, 7], [[6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[9, 6, 4, 3, 5, 2, 1], [5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [9, 5, 3, 8, 6, 1, 7], [[6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 9, 'Tail' = [6, 4, 3, 5, 2, 1], 'Rows' = [[5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], 'Heads' = [5, 3, 8, 6, 1, 7], 'Tails' = [[3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [5, 3, 8, 6, 1, 7], [[3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[5, 3, 1, 2, 9, 8, 6], [3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [5, 3, 8, 6, 1, 7], [[3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 5, 'Tail' = [3, 1, 2, 9, 8, 6], 'Rows' = [[3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], 'Heads' = [3, 8, 6, 1, 7], 'Tails' = [[5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [3, 8, 6, 1, 7], [[5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[3, 5, 8, 6, 7, 4, 2], [8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [3, 8, 6, 1, 7], [[5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 3, 'Tail' = [5, 8, 6, 7, 4, 2], 'Rows' = [[8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], 'Heads' = [8, 6, 1, 7], 'Tails' = [[7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [8, 6, 1, 7], [[7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[8, 7, 9, 4, 1, 3, 5], [6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [8, 6, 1, 7], [[7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 8, 'Tail' = [7, 9, 4, 1, 3, 5], 'Rows' = [[6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], 'Heads' = [6, 1, 7], 'Tails' = [[4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [6, 1, 7], [[4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[6, 4, 7, 8, 2, 1, 9], [1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [6, 1, 7], [[4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 6, 'Tail' = [4, 7, 8, 2, 1, 9], 'Rows' = [[1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], 'Heads' = [1, 7], 'Tails' = [[9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [1, 7], [[9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[1, 9, 3, 5, 8, 6, 7], [7, 2, 6, 1, 3, 5, 4]], [1, 7], [[9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 1, 'Tail' = [9, 3, 5, 8, 6, 7], 'Rows' = [[7, 2, 6, 1, 3, 5, 4]], 'Heads' = [7], 'Tails' = [[2, 6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[7, 2, 6, 1, 3, 5, 4]], [7], [[2, 6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[7, 2, 6, 1, 3, 5, 4]], [7], [[2, 6, 1, 3, 5, 4]]), rule(9), ['Head' = 7, 'Tail' = [2, 6, 1, 3, 5, 4], 'Rows' = [], 'Heads' = [], 'Tails' = []], [sudoku9_heads_tails([], [], [])]). step(sudoku9_transpose([[8, 5, 7, 4, 9, 3], [1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [[8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(7), ['Rows' = [[8, 5, 7, 4, 9, 3], [1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], 'Column' = [8, 1, 6, 3, 5, 7, 4, 9, 2], 'Columns' = [[5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]], 'Tails' = [[5, 7, 4, 9, 3], [2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[8, 5, 7, 4, 9, 3], [1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [8, 1, 6, 3, 5, 7, 4, 9, 2], [[5, 7, 4, 9, 3], [2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]), sudoku9_transpose([[5, 7, 4, 9, 3], [2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [[5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(sudoku9_heads_tails([[8, 5, 7, 4, 9, 3], [1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [8, 1, 6, 3, 5, 7, 4, 9, 2], [[5, 7, 4, 9, 3], [2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]), rule(9), ['Head' = 8, 'Tail' = [5, 7, 4, 9, 3], 'Rows' = [[1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], 'Heads' = [1, 6, 3, 5, 7, 4, 9, 2], 'Tails' = [[2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [1, 6, 3, 5, 7, 4, 9, 2], [[2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [1, 6, 3, 5, 7, 4, 9, 2], [[2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]), rule(9), ['Head' = 1, 'Tail' = [2, 9, 6, 7, 8], 'Rows' = [[6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], 'Heads' = [6, 3, 5, 7, 4, 9, 2], 'Tails' = [[4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [6, 3, 5, 7, 4, 9, 2], [[4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[6, 4, 3, 5, 2, 1], [3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [6, 3, 5, 7, 4, 9, 2], [[4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]), rule(9), ['Head' = 6, 'Tail' = [4, 3, 5, 2, 1], 'Rows' = [[3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], 'Heads' = [3, 5, 7, 4, 9, 2], 'Tails' = [[1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [3, 5, 7, 4, 9, 2], [[1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [3, 5, 7, 4, 9, 2], [[1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]), rule(9), ['Head' = 3, 'Tail' = [1, 2, 9, 8, 6], 'Rows' = [[5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], 'Heads' = [5, 7, 4, 9, 2], 'Tails' = [[8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [5, 7, 4, 9, 2], [[8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [5, 7, 4, 9, 2], [[8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]), rule(9), ['Head' = 5, 'Tail' = [8, 6, 7, 4, 2], 'Rows' = [[7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], 'Heads' = [7, 4, 9, 2], 'Tails' = [[9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [7, 4, 9, 2], [[9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[7, 9, 4, 1, 3, 5], [4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [7, 4, 9, 2], [[9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]), rule(9), ['Head' = 7, 'Tail' = [9, 4, 1, 3, 5], 'Rows' = [[4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], 'Heads' = [4, 9, 2], 'Tails' = [[7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [4, 9, 2], [[7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [4, 9, 2], [[7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]), rule(9), ['Head' = 4, 'Tail' = [7, 8, 2, 1, 9], 'Rows' = [[9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], 'Heads' = [9, 2], 'Tails' = [[3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [9, 2], [[3, 5, 8, 6, 7], [6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]], [9, 2], [[3, 5, 8, 6, 7], [6, 1, 3, 5, 4]]), rule(9), ['Head' = 9, 'Tail' = [3, 5, 8, 6, 7], 'Rows' = [[2, 6, 1, 3, 5, 4]], 'Heads' = [2], 'Tails' = [[6, 1, 3, 5, 4]]], [sudoku9_heads_tails([[2, 6, 1, 3, 5, 4]], [2], [[6, 1, 3, 5, 4]])]). step(sudoku9_heads_tails([[2, 6, 1, 3, 5, 4]], [2], [[6, 1, 3, 5, 4]]), rule(9), ['Head' = 2, 'Tail' = [6, 1, 3, 5, 4], 'Rows' = [], 'Heads' = [], 'Tails' = []], [sudoku9_heads_tails([], [], [])]). step(sudoku9_transpose([[5, 7, 4, 9, 3], [2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [[5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(7), ['Rows' = [[5, 7, 4, 9, 3], [2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], 'Column' = [5, 2, 4, 1, 8, 9, 7, 3, 6], 'Columns' = [[7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]], 'Tails' = [[7, 4, 9, 3], [9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]], [sudoku9_heads_tails([[5, 7, 4, 9, 3], [2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [5, 2, 4, 1, 8, 9, 7, 3, 6], [[7, 4, 9, 3], [9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]), sudoku9_transpose([[7, 4, 9, 3], [9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [[7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(sudoku9_heads_tails([[5, 7, 4, 9, 3], [2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [5, 2, 4, 1, 8, 9, 7, 3, 6], [[7, 4, 9, 3], [9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]), rule(9), ['Head' = 5, 'Tail' = [7, 4, 9, 3], 'Rows' = [[2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], 'Heads' = [2, 4, 1, 8, 9, 7, 3, 6], 'Tails' = [[9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]], [sudoku9_heads_tails([[2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [2, 4, 1, 8, 9, 7, 3, 6], [[9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]])]). step(sudoku9_heads_tails([[2, 9, 6, 7, 8], [4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [2, 4, 1, 8, 9, 7, 3, 6], [[9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]), rule(9), ['Head' = 2, 'Tail' = [9, 6, 7, 8], 'Rows' = [[4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], 'Heads' = [4, 1, 8, 9, 7, 3, 6], 'Tails' = [[3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]], [sudoku9_heads_tails([[4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [4, 1, 8, 9, 7, 3, 6], [[3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]])]). step(sudoku9_heads_tails([[4, 3, 5, 2, 1], [1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [4, 1, 8, 9, 7, 3, 6], [[3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]), rule(9), ['Head' = 4, 'Tail' = [3, 5, 2, 1], 'Rows' = [[1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], 'Heads' = [1, 8, 9, 7, 3, 6], 'Tails' = [[2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]], [sudoku9_heads_tails([[1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [1, 8, 9, 7, 3, 6], [[2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]])]). step(sudoku9_heads_tails([[1, 2, 9, 8, 6], [8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [1, 8, 9, 7, 3, 6], [[2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]), rule(9), ['Head' = 1, 'Tail' = [2, 9, 8, 6], 'Rows' = [[8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], 'Heads' = [8, 9, 7, 3, 6], 'Tails' = [[6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]], [sudoku9_heads_tails([[8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [8, 9, 7, 3, 6], [[6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]])]). step(sudoku9_heads_tails([[8, 6, 7, 4, 2], [9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [8, 9, 7, 3, 6], [[6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]), rule(9), ['Head' = 8, 'Tail' = [6, 7, 4, 2], 'Rows' = [[9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], 'Heads' = [9, 7, 3, 6], 'Tails' = [[4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]], [sudoku9_heads_tails([[9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [9, 7, 3, 6], [[4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]])]). step(sudoku9_heads_tails([[9, 4, 1, 3, 5], [7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [9, 7, 3, 6], [[4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]), rule(9), ['Head' = 9, 'Tail' = [4, 1, 3, 5], 'Rows' = [[7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], 'Heads' = [7, 3, 6], 'Tails' = [[8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]], [sudoku9_heads_tails([[7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [7, 3, 6], [[8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]])]). step(sudoku9_heads_tails([[7, 8, 2, 1, 9], [3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [7, 3, 6], [[8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]]), rule(9), ['Head' = 7, 'Tail' = [8, 2, 1, 9], 'Rows' = [[3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], 'Heads' = [3, 6], 'Tails' = [[5, 8, 6, 7], [1, 3, 5, 4]]], [sudoku9_heads_tails([[3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [3, 6], [[5, 8, 6, 7], [1, 3, 5, 4]])]). step(sudoku9_heads_tails([[3, 5, 8, 6, 7], [6, 1, 3, 5, 4]], [3, 6], [[5, 8, 6, 7], [1, 3, 5, 4]]), rule(9), ['Head' = 3, 'Tail' = [5, 8, 6, 7], 'Rows' = [[6, 1, 3, 5, 4]], 'Heads' = [6], 'Tails' = [[1, 3, 5, 4]]], [sudoku9_heads_tails([[6, 1, 3, 5, 4]], [6], [[1, 3, 5, 4]])]). step(sudoku9_heads_tails([[6, 1, 3, 5, 4]], [6], [[1, 3, 5, 4]]), rule(9), ['Head' = 6, 'Tail' = [1, 3, 5, 4], 'Rows' = [], 'Heads' = [], 'Tails' = []], [sudoku9_heads_tails([], [], [])]). step(sudoku9_transpose([[7, 4, 9, 3], [9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [[7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(7), ['Rows' = [[7, 4, 9, 3], [9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], 'Column' = [7, 9, 3, 2, 6, 4, 8, 5, 1], 'Columns' = [[4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]], 'Tails' = [[4, 9, 3], [6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]], [sudoku9_heads_tails([[7, 4, 9, 3], [9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [7, 9, 3, 2, 6, 4, 8, 5, 1], [[4, 9, 3], [6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]), sudoku9_transpose([[4, 9, 3], [6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [[4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(sudoku9_heads_tails([[7, 4, 9, 3], [9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [7, 9, 3, 2, 6, 4, 8, 5, 1], [[4, 9, 3], [6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]), rule(9), ['Head' = 7, 'Tail' = [4, 9, 3], 'Rows' = [[9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], 'Heads' = [9, 3, 2, 6, 4, 8, 5, 1], 'Tails' = [[6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]], [sudoku9_heads_tails([[9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [9, 3, 2, 6, 4, 8, 5, 1], [[6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]])]). step(sudoku9_heads_tails([[9, 6, 7, 8], [3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [9, 3, 2, 6, 4, 8, 5, 1], [[6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]), rule(9), ['Head' = 9, 'Tail' = [6, 7, 8], 'Rows' = [[3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], 'Heads' = [3, 2, 6, 4, 8, 5, 1], 'Tails' = [[5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]], [sudoku9_heads_tails([[3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [3, 2, 6, 4, 8, 5, 1], [[5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]])]). step(sudoku9_heads_tails([[3, 5, 2, 1], [2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [3, 2, 6, 4, 8, 5, 1], [[5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]), rule(9), ['Head' = 3, 'Tail' = [5, 2, 1], 'Rows' = [[2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], 'Heads' = [2, 6, 4, 8, 5, 1], 'Tails' = [[9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]], [sudoku9_heads_tails([[2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [2, 6, 4, 8, 5, 1], [[9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]])]). step(sudoku9_heads_tails([[2, 9, 8, 6], [6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [2, 6, 4, 8, 5, 1], [[9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]), rule(9), ['Head' = 2, 'Tail' = [9, 8, 6], 'Rows' = [[6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], 'Heads' = [6, 4, 8, 5, 1], 'Tails' = [[7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]], [sudoku9_heads_tails([[6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [6, 4, 8, 5, 1], [[7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]])]). step(sudoku9_heads_tails([[6, 7, 4, 2], [4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [6, 4, 8, 5, 1], [[7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]), rule(9), ['Head' = 6, 'Tail' = [7, 4, 2], 'Rows' = [[4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], 'Heads' = [4, 8, 5, 1], 'Tails' = [[1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]], [sudoku9_heads_tails([[4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [4, 8, 5, 1], [[1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]])]). step(sudoku9_heads_tails([[4, 1, 3, 5], [8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [4, 8, 5, 1], [[1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]]), rule(9), ['Head' = 4, 'Tail' = [1, 3, 5], 'Rows' = [[8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], 'Heads' = [8, 5, 1], 'Tails' = [[2, 1, 9], [8, 6, 7], [3, 5, 4]]], [sudoku9_heads_tails([[8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [8, 5, 1], [[2, 1, 9], [8, 6, 7], [3, 5, 4]])]). step(sudoku9_heads_tails([[8, 2, 1, 9], [5, 8, 6, 7], [1, 3, 5, 4]], [8, 5, 1], [[2, 1, 9], [8, 6, 7], [3, 5, 4]]), rule(9), ['Head' = 8, 'Tail' = [2, 1, 9], 'Rows' = [[5, 8, 6, 7], [1, 3, 5, 4]], 'Heads' = [5, 1], 'Tails' = [[8, 6, 7], [3, 5, 4]]], [sudoku9_heads_tails([[5, 8, 6, 7], [1, 3, 5, 4]], [5, 1], [[8, 6, 7], [3, 5, 4]])]). step(sudoku9_heads_tails([[5, 8, 6, 7], [1, 3, 5, 4]], [5, 1], [[8, 6, 7], [3, 5, 4]]), rule(9), ['Head' = 5, 'Tail' = [8, 6, 7], 'Rows' = [[1, 3, 5, 4]], 'Heads' = [1], 'Tails' = [[3, 5, 4]]], [sudoku9_heads_tails([[1, 3, 5, 4]], [1], [[3, 5, 4]])]). step(sudoku9_heads_tails([[1, 3, 5, 4]], [1], [[3, 5, 4]]), rule(9), ['Head' = 1, 'Tail' = [3, 5, 4], 'Rows' = [], 'Heads' = [], 'Tails' = []], [sudoku9_heads_tails([], [], [])]). step(sudoku9_transpose([[4, 9, 3], [6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [[4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(7), ['Rows' = [[4, 9, 3], [6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], 'Column' = [4, 6, 5, 9, 7, 1, 2, 8, 3], 'Columns' = [[9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]], 'Tails' = [[9, 3], [7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]]], [sudoku9_heads_tails([[4, 9, 3], [6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [4, 6, 5, 9, 7, 1, 2, 8, 3], [[9, 3], [7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]]), sudoku9_transpose([[9, 3], [7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], [[9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(sudoku9_heads_tails([[4, 9, 3], [6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [4, 6, 5, 9, 7, 1, 2, 8, 3], [[9, 3], [7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]]), rule(9), ['Head' = 4, 'Tail' = [9, 3], 'Rows' = [[6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], 'Heads' = [6, 5, 9, 7, 1, 2, 8, 3], 'Tails' = [[7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]]], [sudoku9_heads_tails([[6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [6, 5, 9, 7, 1, 2, 8, 3], [[7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]])]). step(sudoku9_heads_tails([[6, 7, 8], [5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [6, 5, 9, 7, 1, 2, 8, 3], [[7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]]), rule(9), ['Head' = 6, 'Tail' = [7, 8], 'Rows' = [[5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], 'Heads' = [5, 9, 7, 1, 2, 8, 3], 'Tails' = [[2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]]], [sudoku9_heads_tails([[5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [5, 9, 7, 1, 2, 8, 3], [[2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]])]). step(sudoku9_heads_tails([[5, 2, 1], [9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [5, 9, 7, 1, 2, 8, 3], [[2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]]), rule(9), ['Head' = 5, 'Tail' = [2, 1], 'Rows' = [[9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], 'Heads' = [9, 7, 1, 2, 8, 3], 'Tails' = [[8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]]], [sudoku9_heads_tails([[9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [9, 7, 1, 2, 8, 3], [[8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]])]). step(sudoku9_heads_tails([[9, 8, 6], [7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [9, 7, 1, 2, 8, 3], [[8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]]), rule(9), ['Head' = 9, 'Tail' = [8, 6], 'Rows' = [[7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], 'Heads' = [7, 1, 2, 8, 3], 'Tails' = [[4, 2], [3, 5], [1, 9], [6, 7], [5, 4]]], [sudoku9_heads_tails([[7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [7, 1, 2, 8, 3], [[4, 2], [3, 5], [1, 9], [6, 7], [5, 4]])]). step(sudoku9_heads_tails([[7, 4, 2], [1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [7, 1, 2, 8, 3], [[4, 2], [3, 5], [1, 9], [6, 7], [5, 4]]), rule(9), ['Head' = 7, 'Tail' = [4, 2], 'Rows' = [[1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], 'Heads' = [1, 2, 8, 3], 'Tails' = [[3, 5], [1, 9], [6, 7], [5, 4]]], [sudoku9_heads_tails([[1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [1, 2, 8, 3], [[3, 5], [1, 9], [6, 7], [5, 4]])]). step(sudoku9_heads_tails([[1, 3, 5], [2, 1, 9], [8, 6, 7], [3, 5, 4]], [1, 2, 8, 3], [[3, 5], [1, 9], [6, 7], [5, 4]]), rule(9), ['Head' = 1, 'Tail' = [3, 5], 'Rows' = [[2, 1, 9], [8, 6, 7], [3, 5, 4]], 'Heads' = [2, 8, 3], 'Tails' = [[1, 9], [6, 7], [5, 4]]], [sudoku9_heads_tails([[2, 1, 9], [8, 6, 7], [3, 5, 4]], [2, 8, 3], [[1, 9], [6, 7], [5, 4]])]). step(sudoku9_heads_tails([[2, 1, 9], [8, 6, 7], [3, 5, 4]], [2, 8, 3], [[1, 9], [6, 7], [5, 4]]), rule(9), ['Head' = 2, 'Tail' = [1, 9], 'Rows' = [[8, 6, 7], [3, 5, 4]], 'Heads' = [8, 3], 'Tails' = [[6, 7], [5, 4]]], [sudoku9_heads_tails([[8, 6, 7], [3, 5, 4]], [8, 3], [[6, 7], [5, 4]])]). step(sudoku9_heads_tails([[8, 6, 7], [3, 5, 4]], [8, 3], [[6, 7], [5, 4]]), rule(9), ['Head' = 8, 'Tail' = [6, 7], 'Rows' = [[3, 5, 4]], 'Heads' = [3], 'Tails' = [[5, 4]]], [sudoku9_heads_tails([[3, 5, 4]], [3], [[5, 4]])]). step(sudoku9_heads_tails([[3, 5, 4]], [3], [[5, 4]]), rule(9), ['Head' = 3, 'Tail' = [5, 4], 'Rows' = [], 'Heads' = [], 'Tails' = []], [sudoku9_heads_tails([], [], [])]). step(sudoku9_transpose([[9, 3], [7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], [[9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(7), ['Rows' = [[9, 3], [7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], 'Column' = [9, 7, 2, 8, 4, 3, 1, 6, 5], 'Columns' = [[3, 8, 1, 6, 2, 5, 9, 7, 4]], 'Tails' = [[3], [8], [1], [6], [2], [5], [9], [7], [4]]], [sudoku9_heads_tails([[9, 3], [7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], [9, 7, 2, 8, 4, 3, 1, 6, 5], [[3], [8], [1], [6], [2], [5], [9], [7], [4]]), sudoku9_transpose([[3], [8], [1], [6], [2], [5], [9], [7], [4]], [[3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(sudoku9_heads_tails([[9, 3], [7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], [9, 7, 2, 8, 4, 3, 1, 6, 5], [[3], [8], [1], [6], [2], [5], [9], [7], [4]]), rule(9), ['Head' = 9, 'Tail' = [3], 'Rows' = [[7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], 'Heads' = [7, 2, 8, 4, 3, 1, 6, 5], 'Tails' = [[8], [1], [6], [2], [5], [9], [7], [4]]], [sudoku9_heads_tails([[7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], [7, 2, 8, 4, 3, 1, 6, 5], [[8], [1], [6], [2], [5], [9], [7], [4]])]). step(sudoku9_heads_tails([[7, 8], [2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], [7, 2, 8, 4, 3, 1, 6, 5], [[8], [1], [6], [2], [5], [9], [7], [4]]), rule(9), ['Head' = 7, 'Tail' = [8], 'Rows' = [[2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], 'Heads' = [2, 8, 4, 3, 1, 6, 5], 'Tails' = [[1], [6], [2], [5], [9], [7], [4]]], [sudoku9_heads_tails([[2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], [2, 8, 4, 3, 1, 6, 5], [[1], [6], [2], [5], [9], [7], [4]])]). step(sudoku9_heads_tails([[2, 1], [8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], [2, 8, 4, 3, 1, 6, 5], [[1], [6], [2], [5], [9], [7], [4]]), rule(9), ['Head' = 2, 'Tail' = [1], 'Rows' = [[8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], 'Heads' = [8, 4, 3, 1, 6, 5], 'Tails' = [[6], [2], [5], [9], [7], [4]]], [sudoku9_heads_tails([[8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], [8, 4, 3, 1, 6, 5], [[6], [2], [5], [9], [7], [4]])]). step(sudoku9_heads_tails([[8, 6], [4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], [8, 4, 3, 1, 6, 5], [[6], [2], [5], [9], [7], [4]]), rule(9), ['Head' = 8, 'Tail' = [6], 'Rows' = [[4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], 'Heads' = [4, 3, 1, 6, 5], 'Tails' = [[2], [5], [9], [7], [4]]], [sudoku9_heads_tails([[4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], [4, 3, 1, 6, 5], [[2], [5], [9], [7], [4]])]). step(sudoku9_heads_tails([[4, 2], [3, 5], [1, 9], [6, 7], [5, 4]], [4, 3, 1, 6, 5], [[2], [5], [9], [7], [4]]), rule(9), ['Head' = 4, 'Tail' = [2], 'Rows' = [[3, 5], [1, 9], [6, 7], [5, 4]], 'Heads' = [3, 1, 6, 5], 'Tails' = [[5], [9], [7], [4]]], [sudoku9_heads_tails([[3, 5], [1, 9], [6, 7], [5, 4]], [3, 1, 6, 5], [[5], [9], [7], [4]])]). step(sudoku9_heads_tails([[3, 5], [1, 9], [6, 7], [5, 4]], [3, 1, 6, 5], [[5], [9], [7], [4]]), rule(9), ['Head' = 3, 'Tail' = [5], 'Rows' = [[1, 9], [6, 7], [5, 4]], 'Heads' = [1, 6, 5], 'Tails' = [[9], [7], [4]]], [sudoku9_heads_tails([[1, 9], [6, 7], [5, 4]], [1, 6, 5], [[9], [7], [4]])]). step(sudoku9_heads_tails([[1, 9], [6, 7], [5, 4]], [1, 6, 5], [[9], [7], [4]]), rule(9), ['Head' = 1, 'Tail' = [9], 'Rows' = [[6, 7], [5, 4]], 'Heads' = [6, 5], 'Tails' = [[7], [4]]], [sudoku9_heads_tails([[6, 7], [5, 4]], [6, 5], [[7], [4]])]). step(sudoku9_heads_tails([[6, 7], [5, 4]], [6, 5], [[7], [4]]), rule(9), ['Head' = 6, 'Tail' = [7], 'Rows' = [[5, 4]], 'Heads' = [5], 'Tails' = [[4]]], [sudoku9_heads_tails([[5, 4]], [5], [[4]])]). step(sudoku9_heads_tails([[5, 4]], [5], [[4]]), rule(9), ['Head' = 5, 'Tail' = [4], 'Rows' = [], 'Heads' = [], 'Tails' = []], [sudoku9_heads_tails([], [], [])]). step(sudoku9_transpose([[3], [8], [1], [6], [2], [5], [9], [7], [4]], [[3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(7), ['Rows' = [[3], [8], [1], [6], [2], [5], [9], [7], [4]], 'Column' = [3, 8, 1, 6, 2, 5, 9, 7, 4], 'Columns' = [], 'Tails' = [[], [], [], [], [], [], [], [], []]], [sudoku9_heads_tails([[3], [8], [1], [6], [2], [5], [9], [7], [4]], [3, 8, 1, 6, 2, 5, 9, 7, 4], [[], [], [], [], [], [], [], [], []]), sudoku9_transpose([[], [], [], [], [], [], [], [], []], [])]). step(sudoku9_heads_tails([[3], [8], [1], [6], [2], [5], [9], [7], [4]], [3, 8, 1, 6, 2, 5, 9, 7, 4], [[], [], [], [], [], [], [], [], []]), rule(9), ['Head' = 3, 'Tail' = [], 'Rows' = [[8], [1], [6], [2], [5], [9], [7], [4]], 'Heads' = [8, 1, 6, 2, 5, 9, 7, 4], 'Tails' = [[], [], [], [], [], [], [], []]], [sudoku9_heads_tails([[8], [1], [6], [2], [5], [9], [7], [4]], [8, 1, 6, 2, 5, 9, 7, 4], [[], [], [], [], [], [], [], []])]). step(sudoku9_heads_tails([[8], [1], [6], [2], [5], [9], [7], [4]], [8, 1, 6, 2, 5, 9, 7, 4], [[], [], [], [], [], [], [], []]), rule(9), ['Head' = 8, 'Tail' = [], 'Rows' = [[1], [6], [2], [5], [9], [7], [4]], 'Heads' = [1, 6, 2, 5, 9, 7, 4], 'Tails' = [[], [], [], [], [], [], []]], [sudoku9_heads_tails([[1], [6], [2], [5], [9], [7], [4]], [1, 6, 2, 5, 9, 7, 4], [[], [], [], [], [], [], []])]). step(sudoku9_heads_tails([[1], [6], [2], [5], [9], [7], [4]], [1, 6, 2, 5, 9, 7, 4], [[], [], [], [], [], [], []]), rule(9), ['Head' = 1, 'Tail' = [], 'Rows' = [[6], [2], [5], [9], [7], [4]], 'Heads' = [6, 2, 5, 9, 7, 4], 'Tails' = [[], [], [], [], [], []]], [sudoku9_heads_tails([[6], [2], [5], [9], [7], [4]], [6, 2, 5, 9, 7, 4], [[], [], [], [], [], []])]). step(sudoku9_heads_tails([[6], [2], [5], [9], [7], [4]], [6, 2, 5, 9, 7, 4], [[], [], [], [], [], []]), rule(9), ['Head' = 6, 'Tail' = [], 'Rows' = [[2], [5], [9], [7], [4]], 'Heads' = [2, 5, 9, 7, 4], 'Tails' = [[], [], [], [], []]], [sudoku9_heads_tails([[2], [5], [9], [7], [4]], [2, 5, 9, 7, 4], [[], [], [], [], []])]). step(sudoku9_heads_tails([[2], [5], [9], [7], [4]], [2, 5, 9, 7, 4], [[], [], [], [], []]), rule(9), ['Head' = 2, 'Tail' = [], 'Rows' = [[5], [9], [7], [4]], 'Heads' = [5, 9, 7, 4], 'Tails' = [[], [], [], []]], [sudoku9_heads_tails([[5], [9], [7], [4]], [5, 9, 7, 4], [[], [], [], []])]). step(sudoku9_heads_tails([[5], [9], [7], [4]], [5, 9, 7, 4], [[], [], [], []]), rule(9), ['Head' = 5, 'Tail' = [], 'Rows' = [[9], [7], [4]], 'Heads' = [9, 7, 4], 'Tails' = [[], [], []]], [sudoku9_heads_tails([[9], [7], [4]], [9, 7, 4], [[], [], []])]). step(sudoku9_heads_tails([[9], [7], [4]], [9, 7, 4], [[], [], []]), rule(9), ['Head' = 9, 'Tail' = [], 'Rows' = [[7], [4]], 'Heads' = [7, 4], 'Tails' = [[], []]], [sudoku9_heads_tails([[7], [4]], [7, 4], [[], []])]). step(sudoku9_heads_tails([[7], [4]], [7, 4], [[], []]), rule(9), ['Head' = 7, 'Tail' = [], 'Rows' = [[4]], 'Heads' = [4], 'Tails' = [[]]], [sudoku9_heads_tails([[4]], [4], [[]])]). step(sudoku9_heads_tails([[4]], [4], [[]]), rule(9), ['Head' = 4, 'Tail' = [], 'Rows' = [], 'Heads' = [], 'Tails' = []], [sudoku9_heads_tails([], [], [])]). step(sudoku9_transpose([[], [], [], [], [], [], [], [], []], []), fact(6), [], []). step(sudoku9_rows_distinct([[1, 5, 7, 4, 9, 6, 3, 2, 8], [6, 3, 8, 7, 1, 2, 5, 4, 9], [2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(5), ['Row' = [1, 5, 7, 4, 9, 6, 3, 2, 8], 'Rows' = [[6, 3, 8, 7, 1, 2, 5, 4, 9], [2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]], [all_distinct([1, 5, 7, 4, 9, 6, 3, 2, 8]), sudoku9_rows_distinct([[6, 3, 8, 7, 1, 2, 5, 4, 9], [2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(all_distinct([1, 5, 7, 4, 9, 6, 3, 2, 8]), builtin, [], []). step(sudoku9_rows_distinct([[6, 3, 8, 7, 1, 2, 5, 4, 9], [2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(5), ['Row' = [6, 3, 8, 7, 1, 2, 5, 4, 9], 'Rows' = [[2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]], [all_distinct([6, 3, 8, 7, 1, 2, 5, 4, 9]), sudoku9_rows_distinct([[2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(all_distinct([6, 3, 8, 7, 1, 2, 5, 4, 9]), builtin, [], []). step(sudoku9_rows_distinct([[2, 4, 9, 5, 3, 8, 6, 1, 7], [8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(5), ['Row' = [2, 4, 9, 5, 3, 8, 6, 1, 7], 'Rows' = [[8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]], [all_distinct([2, 4, 9, 5, 3, 8, 6, 1, 7]), sudoku9_rows_distinct([[8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(all_distinct([2, 4, 9, 5, 3, 8, 6, 1, 7]), builtin, [], []). step(sudoku9_rows_distinct([[8, 1, 6, 3, 5, 7, 4, 9, 2], [5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(5), ['Row' = [8, 1, 6, 3, 5, 7, 4, 9, 2], 'Rows' = [[5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]], [all_distinct([8, 1, 6, 3, 5, 7, 4, 9, 2]), sudoku9_rows_distinct([[5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(all_distinct([8, 1, 6, 3, 5, 7, 4, 9, 2]), builtin, [], []). step(sudoku9_rows_distinct([[5, 2, 4, 1, 8, 9, 7, 3, 6], [7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(5), ['Row' = [5, 2, 4, 1, 8, 9, 7, 3, 6], 'Rows' = [[7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]], [all_distinct([5, 2, 4, 1, 8, 9, 7, 3, 6]), sudoku9_rows_distinct([[7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(all_distinct([5, 2, 4, 1, 8, 9, 7, 3, 6]), builtin, [], []). step(sudoku9_rows_distinct([[7, 9, 3, 2, 6, 4, 8, 5, 1], [4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(5), ['Row' = [7, 9, 3, 2, 6, 4, 8, 5, 1], 'Rows' = [[4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]], [all_distinct([7, 9, 3, 2, 6, 4, 8, 5, 1]), sudoku9_rows_distinct([[4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(all_distinct([7, 9, 3, 2, 6, 4, 8, 5, 1]), builtin, [], []). step(sudoku9_rows_distinct([[4, 6, 5, 9, 7, 1, 2, 8, 3], [9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(5), ['Row' = [4, 6, 5, 9, 7, 1, 2, 8, 3], 'Rows' = [[9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]], [all_distinct([4, 6, 5, 9, 7, 1, 2, 8, 3]), sudoku9_rows_distinct([[9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(all_distinct([4, 6, 5, 9, 7, 1, 2, 8, 3]), builtin, [], []). step(sudoku9_rows_distinct([[9, 7, 2, 8, 4, 3, 1, 6, 5], [3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(5), ['Row' = [9, 7, 2, 8, 4, 3, 1, 6, 5], 'Rows' = [[3, 8, 1, 6, 2, 5, 9, 7, 4]]], [all_distinct([9, 7, 2, 8, 4, 3, 1, 6, 5]), sudoku9_rows_distinct([[3, 8, 1, 6, 2, 5, 9, 7, 4]])]). step(all_distinct([9, 7, 2, 8, 4, 3, 1, 6, 5]), builtin, [], []). step(sudoku9_rows_distinct([[3, 8, 1, 6, 2, 5, 9, 7, 4]]), rule(5), ['Row' = [3, 8, 1, 6, 2, 5, 9, 7, 4], 'Rows' = []], [all_distinct([3, 8, 1, 6, 2, 5, 9, 7, 4]), sudoku9_rows_distinct([])]). step(all_distinct([3, 8, 1, 6, 2, 5, 9, 7, 4]), builtin, [], []). step(sudoku9_rows_distinct([]), fact(4), [], []). step(sudoku9_blocks([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(11), ['A' = [1, 6, 2, 8, 5, 7, 4, 9, 3], 'B' = [5, 3, 4, 1, 2, 9, 6, 7, 8], 'C' = [7, 8, 9, 6, 4, 3, 5, 2, 1], 'Rows' = [[4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]], [sudoku9_block_row([1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1]), sudoku9_blocks([[4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_block_row([1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1]), rule(13), ['A' = 1, 'B' = 6, 'C' = 2, 'As' = [8, 5, 7, 4, 9, 3], 'D' = 5, 'E' = 3, 'F' = 4, 'Bs' = [1, 2, 9, 6, 7, 8], 'G' = 7, 'H' = 8, 'I' = 9, 'Cs' = [6, 4, 3, 5, 2, 1]], [all_distinct([1, 6, 2, 5, 3, 4, 7, 8, 9]), sudoku9_block_row([8, 5, 7, 4, 9, 3], [1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1])]). step(all_distinct([1, 6, 2, 5, 3, 4, 7, 8, 9]), builtin, [], []). step(sudoku9_block_row([8, 5, 7, 4, 9, 3], [1, 2, 9, 6, 7, 8], [6, 4, 3, 5, 2, 1]), rule(13), ['A' = 8, 'B' = 5, 'C' = 7, 'As' = [4, 9, 3], 'D' = 1, 'E' = 2, 'F' = 9, 'Bs' = [6, 7, 8], 'G' = 6, 'H' = 4, 'I' = 3, 'Cs' = [5, 2, 1]], [all_distinct([8, 5, 7, 1, 2, 9, 6, 4, 3]), sudoku9_block_row([4, 9, 3], [6, 7, 8], [5, 2, 1])]). step(all_distinct([8, 5, 7, 1, 2, 9, 6, 4, 3]), builtin, [], []). step(sudoku9_block_row([4, 9, 3], [6, 7, 8], [5, 2, 1]), rule(13), ['A' = 4, 'B' = 9, 'C' = 3, 'As' = [], 'D' = 6, 'E' = 7, 'F' = 8, 'Bs' = [], 'G' = 5, 'H' = 2, 'I' = 1, 'Cs' = []], [all_distinct([4, 9, 3, 6, 7, 8, 5, 2, 1]), sudoku9_block_row([], [], [])]). step(all_distinct([4, 9, 3, 6, 7, 8, 5, 2, 1]), builtin, [], []). step(sudoku9_block_row([], [], []), fact(12), [], []). step(sudoku9_blocks([[4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(11), ['A' = [4, 7, 5, 3, 1, 2, 9, 8, 6], 'B' = [9, 1, 3, 5, 8, 6, 7, 4, 2], 'C' = [6, 2, 8, 7, 9, 4, 1, 3, 5], 'Rows' = [[3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]], [sudoku9_block_row([4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5]), sudoku9_blocks([[3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]])]). step(sudoku9_block_row([4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5]), rule(13), ['A' = 4, 'B' = 7, 'C' = 5, 'As' = [3, 1, 2, 9, 8, 6], 'D' = 9, 'E' = 1, 'F' = 3, 'Bs' = [5, 8, 6, 7, 4, 2], 'G' = 6, 'H' = 2, 'I' = 8, 'Cs' = [7, 9, 4, 1, 3, 5]], [all_distinct([4, 7, 5, 9, 1, 3, 6, 2, 8]), sudoku9_block_row([3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5])]). step(all_distinct([4, 7, 5, 9, 1, 3, 6, 2, 8]), builtin, [], []). step(sudoku9_block_row([3, 1, 2, 9, 8, 6], [5, 8, 6, 7, 4, 2], [7, 9, 4, 1, 3, 5]), rule(13), ['A' = 3, 'B' = 1, 'C' = 2, 'As' = [9, 8, 6], 'D' = 5, 'E' = 8, 'F' = 6, 'Bs' = [7, 4, 2], 'G' = 7, 'H' = 9, 'I' = 4, 'Cs' = [1, 3, 5]], [all_distinct([3, 1, 2, 5, 8, 6, 7, 9, 4]), sudoku9_block_row([9, 8, 6], [7, 4, 2], [1, 3, 5])]). step(all_distinct([3, 1, 2, 5, 8, 6, 7, 9, 4]), builtin, [], []). step(sudoku9_block_row([9, 8, 6], [7, 4, 2], [1, 3, 5]), rule(13), ['A' = 9, 'B' = 8, 'C' = 6, 'As' = [], 'D' = 7, 'E' = 4, 'F' = 2, 'Bs' = [], 'G' = 1, 'H' = 3, 'I' = 5, 'Cs' = []], [all_distinct([9, 8, 6, 7, 4, 2, 1, 3, 5]), sudoku9_block_row([], [], [])]). step(all_distinct([9, 8, 6, 7, 4, 2, 1, 3, 5]), builtin, [], []). step(sudoku9_blocks([[3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]]), rule(11), ['A' = [3, 5, 6, 4, 7, 8, 2, 1, 9], 'B' = [2, 4, 1, 9, 3, 5, 8, 6, 7], 'C' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Rows' = []], [sudoku9_block_row([3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]), sudoku9_blocks([])]). step(sudoku9_block_row([3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(13), ['A' = 3, 'B' = 5, 'C' = 6, 'As' = [4, 7, 8, 2, 1, 9], 'D' = 2, 'E' = 4, 'F' = 1, 'Bs' = [9, 3, 5, 8, 6, 7], 'G' = 8, 'H' = 9, 'I' = 7, 'Cs' = [2, 6, 1, 3, 5, 4]], [all_distinct([3, 5, 6, 2, 4, 1, 8, 9, 7]), sudoku9_block_row([4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4])]). step(all_distinct([3, 5, 6, 2, 4, 1, 8, 9, 7]), builtin, [], []). step(sudoku9_block_row([4, 7, 8, 2, 1, 9], [9, 3, 5, 8, 6, 7], [2, 6, 1, 3, 5, 4]), rule(13), ['A' = 4, 'B' = 7, 'C' = 8, 'As' = [2, 1, 9], 'D' = 9, 'E' = 3, 'F' = 5, 'Bs' = [8, 6, 7], 'G' = 2, 'H' = 6, 'I' = 1, 'Cs' = [3, 5, 4]], [all_distinct([4, 7, 8, 9, 3, 5, 2, 6, 1]), sudoku9_block_row([2, 1, 9], [8, 6, 7], [3, 5, 4])]). step(all_distinct([4, 7, 8, 9, 3, 5, 2, 6, 1]), builtin, [], []). step(sudoku9_block_row([2, 1, 9], [8, 6, 7], [3, 5, 4]), rule(13), ['A' = 2, 'B' = 1, 'C' = 9, 'As' = [], 'D' = 8, 'E' = 6, 'F' = 7, 'Bs' = [], 'G' = 3, 'H' = 5, 'I' = 4, 'Cs' = []], [all_distinct([2, 1, 9, 8, 6, 7, 3, 5, 4]), sudoku9_block_row([], [], [])]). step(all_distinct([2, 1, 9, 8, 6, 7, 3, 5, 4]), builtin, [], []). step(sudoku9_blocks([]), fact(10), [], []). step(sudoku9_flatten([[1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [1, 6, 2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(15), ['Row' = [1, 6, 2, 8, 5, 7, 4, 9, 3], 'Rows' = [[5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Cells' = [1, 6, 2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Rest' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 6, 2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), sudoku9_flatten([[5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([1, 6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 6, 2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 1, 'Xs' = [6, 2, 8, 5, 7, 4, 9, 3], 'Ys' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [6, 2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([6, 2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 6, 'Xs' = [2, 8, 5, 7, 4, 9, 3], 'Ys' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([2, 8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 2, 'Xs' = [8, 5, 7, 4, 9, 3], 'Ys' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([8, 5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 8, 'Xs' = [5, 7, 4, 9, 3], 'Ys' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([5, 7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 5, 'Xs' = [7, 4, 9, 3], 'Ys' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([7, 4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 7, 'Xs' = [4, 9, 3], 'Ys' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([4, 9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 4, 'Xs' = [9, 3], 'Ys' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([9, 3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 9, 'Xs' = [3], 'Ys' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([3], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 3, 'Xs' = [], 'Ys' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), fact(16), ['Ys' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], []). step(sudoku9_flatten([[5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(15), ['Row' = [5, 3, 4, 1, 2, 9, 6, 7, 8], 'Rows' = [[7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Cells' = [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Rest' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), sudoku9_flatten([[7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([5, 3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 5, 'Xs' = [3, 4, 1, 2, 9, 6, 7, 8], 'Ys' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([3, 4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 3, 'Xs' = [4, 1, 2, 9, 6, 7, 8], 'Ys' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([4, 1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 4, 'Xs' = [1, 2, 9, 6, 7, 8], 'Ys' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([1, 2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 1, 'Xs' = [2, 9, 6, 7, 8], 'Ys' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([2, 9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 2, 'Xs' = [9, 6, 7, 8], 'Ys' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([9, 6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 9, 'Xs' = [6, 7, 8], 'Ys' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([6, 7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 6, 'Xs' = [7, 8], 'Ys' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([7, 8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 7, 'Xs' = [8], 'Ys' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([8], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 8, 'Xs' = [], 'Ys' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), fact(16), ['Ys' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], []). step(sudoku9_flatten([[7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(15), ['Row' = [7, 8, 9, 6, 4, 3, 5, 2, 1], 'Rows' = [[4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Cells' = [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Rest' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), sudoku9_flatten([[4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([7, 8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 7, 'Xs' = [8, 9, 6, 4, 3, 5, 2, 1], 'Ys' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([8, 9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 8, 'Xs' = [9, 6, 4, 3, 5, 2, 1], 'Ys' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([9, 6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 9, 'Xs' = [6, 4, 3, 5, 2, 1], 'Ys' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([6, 4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 6, 'Xs' = [4, 3, 5, 2, 1], 'Ys' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([4, 3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 4, 'Xs' = [3, 5, 2, 1], 'Ys' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([3, 5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 3, 'Xs' = [5, 2, 1], 'Ys' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([5, 2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 5, 'Xs' = [2, 1], 'Ys' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([2, 1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 2, 'Xs' = [1], 'Ys' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([1], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 1, 'Xs' = [], 'Ys' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), fact(16), ['Ys' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], []). step(sudoku9_flatten([[4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(15), ['Row' = [4, 7, 5, 3, 1, 2, 9, 8, 6], 'Rows' = [[9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Cells' = [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Rest' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), sudoku9_flatten([[9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([4, 7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 4, 'Xs' = [7, 5, 3, 1, 2, 9, 8, 6], 'Ys' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([7, 5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 7, 'Xs' = [5, 3, 1, 2, 9, 8, 6], 'Ys' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([5, 3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 5, 'Xs' = [3, 1, 2, 9, 8, 6], 'Ys' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([3, 1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 3, 'Xs' = [1, 2, 9, 8, 6], 'Ys' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([1, 2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 1, 'Xs' = [2, 9, 8, 6], 'Ys' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([2, 9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 2, 'Xs' = [9, 8, 6], 'Ys' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([9, 8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 9, 'Xs' = [8, 6], 'Ys' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([8, 6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 8, 'Xs' = [6], 'Ys' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([6], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 6, 'Xs' = [], 'Ys' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), fact(16), ['Ys' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], []). step(sudoku9_flatten([[9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(15), ['Row' = [9, 1, 3, 5, 8, 6, 7, 4, 2], 'Rows' = [[6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Cells' = [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Rest' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), sudoku9_flatten([[6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([9, 1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 9, 'Xs' = [1, 3, 5, 8, 6, 7, 4, 2], 'Ys' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([1, 3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 1, 'Xs' = [3, 5, 8, 6, 7, 4, 2], 'Ys' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([3, 5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 3, 'Xs' = [5, 8, 6, 7, 4, 2], 'Ys' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([5, 8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 5, 'Xs' = [8, 6, 7, 4, 2], 'Ys' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([8, 6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 8, 'Xs' = [6, 7, 4, 2], 'Ys' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([6, 7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 6, 'Xs' = [7, 4, 2], 'Ys' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([7, 4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 7, 'Xs' = [4, 2], 'Ys' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([4, 2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 4, 'Xs' = [2], 'Ys' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([2], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 2, 'Xs' = [], 'Ys' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), fact(16), ['Ys' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], []). step(sudoku9_flatten([[6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(15), ['Row' = [6, 2, 8, 7, 9, 4, 1, 3, 5], 'Rows' = [[3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Cells' = [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Rest' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), sudoku9_flatten([[3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([6, 2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 6, 'Xs' = [2, 8, 7, 9, 4, 1, 3, 5], 'Ys' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([2, 8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 2, 'Xs' = [8, 7, 9, 4, 1, 3, 5], 'Ys' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([8, 7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 8, 'Xs' = [7, 9, 4, 1, 3, 5], 'Ys' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([7, 9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 7, 'Xs' = [9, 4, 1, 3, 5], 'Ys' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([9, 4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 9, 'Xs' = [4, 1, 3, 5], 'Ys' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([4, 1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 4, 'Xs' = [1, 3, 5], 'Ys' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([1, 3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 1, 'Xs' = [3, 5], 'Ys' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([3, 5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 3, 'Xs' = [5], 'Ys' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([5], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 5, 'Xs' = [], 'Ys' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), fact(16), ['Ys' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], []). step(sudoku9_flatten([[3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(15), ['Row' = [3, 5, 6, 4, 7, 8, 2, 1, 9], 'Rows' = [[2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Cells' = [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Rest' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), sudoku9_flatten([[2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([3, 5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 3, 'Xs' = [5, 6, 4, 7, 8, 2, 1, 9], 'Ys' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([5, 6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 5, 'Xs' = [6, 4, 7, 8, 2, 1, 9], 'Ys' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([6, 4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 6, 'Xs' = [4, 7, 8, 2, 1, 9], 'Ys' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([4, 7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 4, 'Xs' = [7, 8, 2, 1, 9], 'Ys' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([7, 8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 7, 'Xs' = [8, 2, 1, 9], 'Ys' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([8, 2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 8, 'Xs' = [2, 1, 9], 'Ys' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([2, 1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 2, 'Xs' = [1, 9], 'Ys' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([1, 9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 1, 'Xs' = [9], 'Ys' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([9], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 9, 'Xs' = [], 'Ys' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), fact(16), ['Ys' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], []). step(sudoku9_flatten([[2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4]], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(15), ['Row' = [2, 4, 1, 9, 3, 5, 8, 6, 7], 'Rows' = [[8, 9, 7, 2, 6, 1, 3, 5, 4]], 'Cells' = [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4], 'Rest' = [8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), sudoku9_flatten([[8, 9, 7, 2, 6, 1, 3, 5, 4]], [8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([2, 4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 2, 'Xs' = [4, 1, 9, 3, 5, 8, 6, 7], 'Ys' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([4, 1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 4, 'Xs' = [1, 9, 3, 5, 8, 6, 7], 'Ys' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([1, 9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 1, 'Xs' = [9, 3, 5, 8, 6, 7], 'Ys' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([9, 3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 9, 'Xs' = [3, 5, 8, 6, 7], 'Ys' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([3, 5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 3, 'Xs' = [5, 8, 6, 7], 'Ys' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([5, 8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 5, 'Xs' = [8, 6, 7], 'Ys' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([8, 6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 8, 'Xs' = [6, 7], 'Ys' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([6, 7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 6, 'Xs' = [7], 'Ys' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [7, 8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([7], [8, 9, 7, 2, 6, 1, 3, 5, 4], [7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 7, 'Xs' = [], 'Ys' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Zs' = [8, 9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([], [8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([], [8, 9, 7, 2, 6, 1, 3, 5, 4], [8, 9, 7, 2, 6, 1, 3, 5, 4]), fact(16), ['Ys' = [8, 9, 7, 2, 6, 1, 3, 5, 4]], []). step(sudoku9_flatten([[8, 9, 7, 2, 6, 1, 3, 5, 4]], [8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(15), ['Row' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Rows' = [], 'Cells' = [8, 9, 7, 2, 6, 1, 3, 5, 4], 'Rest' = []], [sudoku9_append([8, 9, 7, 2, 6, 1, 3, 5, 4], [], [8, 9, 7, 2, 6, 1, 3, 5, 4]), sudoku9_flatten([], [])]). step(sudoku9_append([8, 9, 7, 2, 6, 1, 3, 5, 4], [], [8, 9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 8, 'Xs' = [9, 7, 2, 6, 1, 3, 5, 4], 'Ys' = [], 'Zs' = [9, 7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([9, 7, 2, 6, 1, 3, 5, 4], [], [9, 7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([9, 7, 2, 6, 1, 3, 5, 4], [], [9, 7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 9, 'Xs' = [7, 2, 6, 1, 3, 5, 4], 'Ys' = [], 'Zs' = [7, 2, 6, 1, 3, 5, 4]], [sudoku9_append([7, 2, 6, 1, 3, 5, 4], [], [7, 2, 6, 1, 3, 5, 4])]). step(sudoku9_append([7, 2, 6, 1, 3, 5, 4], [], [7, 2, 6, 1, 3, 5, 4]), rule(17), ['X' = 7, 'Xs' = [2, 6, 1, 3, 5, 4], 'Ys' = [], 'Zs' = [2, 6, 1, 3, 5, 4]], [sudoku9_append([2, 6, 1, 3, 5, 4], [], [2, 6, 1, 3, 5, 4])]). step(sudoku9_append([2, 6, 1, 3, 5, 4], [], [2, 6, 1, 3, 5, 4]), rule(17), ['X' = 2, 'Xs' = [6, 1, 3, 5, 4], 'Ys' = [], 'Zs' = [6, 1, 3, 5, 4]], [sudoku9_append([6, 1, 3, 5, 4], [], [6, 1, 3, 5, 4])]). step(sudoku9_append([6, 1, 3, 5, 4], [], [6, 1, 3, 5, 4]), rule(17), ['X' = 6, 'Xs' = [1, 3, 5, 4], 'Ys' = [], 'Zs' = [1, 3, 5, 4]], [sudoku9_append([1, 3, 5, 4], [], [1, 3, 5, 4])]). step(sudoku9_append([1, 3, 5, 4], [], [1, 3, 5, 4]), rule(17), ['X' = 1, 'Xs' = [3, 5, 4], 'Ys' = [], 'Zs' = [3, 5, 4]], [sudoku9_append([3, 5, 4], [], [3, 5, 4])]). step(sudoku9_append([3, 5, 4], [], [3, 5, 4]), rule(17), ['X' = 3, 'Xs' = [5, 4], 'Ys' = [], 'Zs' = [5, 4]], [sudoku9_append([5, 4], [], [5, 4])]). step(sudoku9_append([5, 4], [], [5, 4]), rule(17), ['X' = 5, 'Xs' = [4], 'Ys' = [], 'Zs' = [4]], [sudoku9_append([4], [], [4])]). step(sudoku9_append([4], [], [4]), rule(17), ['X' = 4, 'Xs' = [], 'Ys' = [], 'Zs' = []], [sudoku9_append([], [], [])]). step(sudoku9_append([], [], []), fact(16), ['Ys' = []], []). step(sudoku9_flatten([], []), fact(14), [], []). step(labeling([ff], [1, 6, 2, 8, 5, 7, 4, 9, 3, 5, 3, 4, 1, 2, 9, 6, 7, 8, 7, 8, 9, 6, 4, 3, 5, 2, 1, 4, 7, 5, 3, 1, 2, 9, 8, 6, 9, 1, 3, 5, 8, 6, 7, 4, 2, 6, 2, 8, 7, 9, 4, 1, 3, 5, 3, 5, 6, 4, 7, 8, 2, 1, 9, 2, 4, 1, 9, 3, 5, 8, 6, 7, 8, 9, 7, 2, 6, 1, 3, 5, 4]), builtin, [], []).