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optimization: this is cheaper than requiring 'a' not being zero, but the\n // benefit is lost if 'b' is also tested.\n // See: https://github.com/OpenZeppelin/openzeppelin-solidity/pull/522\n if (a == 0) {\n return 0;\n }\n\n uint256 c = a * b;\n require(c / a == b);\n\n return c;\n }\n\n /**\n * @dev Integer division of two unsigned integers truncating the quotient, reverts on division by zero.\n */\n function div(uint256 a, uint256 b) internal pure returns (uint256) {\n // Solidity only automatically asserts when dividing by 0\n require(b > 0);\n uint256 c = a / b;\n // assert(a == b * c + a % b); // There is no case in which this doesn't hold\n\n return c;\n }\n\n /**\n * @dev Subtracts two unsigned integers, reverts on overflow (i.e. if subtrahend is greater than minuend).\n */\n function sub(uint256 a, uint256 b) internal pure returns (uint256) {\n require(b <= a);\n uint256 c = a - b;\n\n return c;\n }\n\n /**\n * @dev Adds two unsigned integers, reverts on overflow.\n */\n 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