import type { Digit } from "../utils";
type AddDigitTable = [
    [
        [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9
        ],
        [
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            0
        ],
        [
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            0,
            1
        ],
        [
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            0,
            1,
            2
        ],
        [
            4,
            5,
            6,
            7,
            8,
            9,
            0,
            1,
            2,
            3
        ],
        [
            5,
            6,
            7,
            8,
            9,
            0,
            1,
            2,
            3,
            4
        ],
        [
            6,
            7,
            8,
            9,
            0,
            1,
            2,
            3,
            4,
            5
        ],
        [
            7,
            8,
            9,
            0,
            1,
            2,
            3,
            4,
            5,
            6
        ],
        [
            8,
            9,
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7
        ],
        [
            9,
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8
        ]
    ],
    [
        [
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            0
        ],
        [
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            0,
            1
        ],
        [
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            0,
            1,
            2
        ],
        [
            4,
            5,
            6,
            7,
            8,
            9,
            0,
            1,
            2,
            3
        ],
        [
            5,
            6,
            7,
            8,
            9,
            0,
            1,
            2,
            3,
            4
        ],
        [
            6,
            7,
            8,
            9,
            0,
            1,
            2,
            3,
            4,
            5
        ],
        [
            7,
            8,
            9,
            0,
            1,
            2,
            3,
            4,
            5,
            6
        ],
        [
            8,
            9,
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7
        ],
        [
            9,
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8
        ],
        [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9
        ]
    ]
];
type AddDigitCarryTable = [
    [
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0
        ],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1
        ],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1
        ],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            1
        ],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            1,
            1
        ],
        [
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            1,
            1,
            1
        ],
        [
            0,
            0,
            0,
            0,
            1,
            1,
            1,
            1,
            1,
            1
        ],
        [
            0,
            0,
            0,
            1,
            1,
            1,
            1,
            1,
            1,
            1
        ],
        [
            0,
            0,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1
        ],
        [
            0,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1
        ]
    ],
    [
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1
        ],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1
        ],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            1
        ],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            1,
            1
        ],
        [
            0,
            0,
            0,
            0,
            0,
            1,
            1,
            1,
            1,
            1
        ],
        [
            0,
            0,
            0,
            0,
            1,
            1,
            1,
            1,
            1,
            1
        ],
        [
            0,
            0,
            0,
            1,
            1,
            1,
            1,
            1,
            1,
            1
        ],
        [
            0,
            0,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1
        ],
        [
            0,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1
        ],
        [
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            1
        ]
    ]
];
type AddDigit<T extends Digit, U extends Digit, Carry extends 0 | 1 = 0> = AddDigitTable[Carry][T][U];
type AddCarryDigit<T extends Digit, U extends Digit, Carry extends 0 | 1 = 0> = AddDigitCarryTable[Carry][T][U];
export type AddDigits<T extends Digit[], U extends Digit[], Carry extends 0 | 1 = 0, Acc extends Digit[] = []> = T extends [...infer R extends Digit[], infer N extends Digit] ? U extends [...infer S extends Digit[], infer M extends Digit] ? AddDigits<R, S, AddCarryDigit<N, M, Carry>, [
    AddDigit<N, M, Carry>,
    ...Acc
]> : AddDigits<R, [
], AddCarryDigit<N, 0, Carry>, [
    AddDigit<N, 0, Carry>,
    ...Acc
]> : U extends [...infer S extends Digit[], infer M extends Digit] ? AddDigits<[
], S, AddCarryDigit<0, M, Carry>, [
    AddDigit<0, M, Carry>,
    ...Acc
]> : Carry extends 1 ? [1, ...Acc] : Acc;
export {};