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51/**
52 * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
53 * overflow (when the result is negative).
54 *
55 * Counterpart to Solidity's `-` operator.
56 *
57 * Requirements:
58 * - Subtraction cannot overflow.
59 *
60 * _Available since v2.4.0._
61 */
62function sub(
63    uint256 a,
64    uint256 b,
65    string memory errorMessage
66) internal pure returns (uint256) {
67    require(b <= a, errorMessage);
68    uint256 c = a - b;
69
70    return c;
71}
72
73/**
74 * @dev Returns the multiplication of two unsigned integers, reverting on
75 * overflow.
76 *
77 * Counterpart to Solidity's `*` operator.
78 *
79 * Requirements:
80 * - Multiplication cannot overflow.
81 */
82function mul(uint256 a, uint256 b) internal pure returns (uint256) {
83    // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
84    // benefit is lost if 'b' is also tested.
85    // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
86    if (a == 0) {
87        return 0;
88    }
89
90    uint256 c = a * b;
91    require(c / a == b, "mul overflow");
92
93    return c;
94}