library SafeMath {
        /**
         * @dev Returns the addition of two unsigned integers, reverting on
         * overflow.
         *
         * Counterpart to Solidity's `+` operator.
         *
         * Requirements:
         *
         * - Addition cannot overflow.
         */
        function add(uint256 a, uint256 b) internal pure returns (uint256) {
            uint256 c = a + b;
            require(c >= a, "SafeMath: addition overflow");
    
            return c;
        }
    
        /**
         * @dev Returns the subtraction of two unsigned integers, reverting on
         * overflow (when the result is negative).
         *
         * Counterpart to Solidity's `-` operator.
         *
         * Requirements:
         *
         * - Subtraction cannot overflow.
         */
        function sub(uint256 a, uint256 b) internal pure returns (uint256) {
            return sub(a, b, "SafeMath: subtraction overflow");
        }
    
        /**
         * @dev Returns the subtraction of two unsigned integers, reverting with custom message on
         * overflow (when the result is negative).
         *
         * Counterpart to Solidity's `-` operator.
         *
         * Requirements:
         *
         * - Subtraction cannot overflow.
         */
        function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
            require(b <= a, errorMessage);
            uint256 c = a - b;
    
            return c;
        }
    
        /**
         * @dev Returns the multiplication of two unsigned integers, reverting on
         * overflow.
         *
         * Counterpart to Solidity's `*` operator.
         *
         * Requirements:
         *
         * - Multiplication cannot overflow.
         */
        function mul(uint256 a, uint256 b) internal pure returns (uint256) {
            // Gas optimization: this is cheaper than requiring 'a' not being zero, but the
            // benefit is lost if 'b' is also tested.
            // See: https://github.com/OpenZeppelin/openzeppelin-contracts/pull/522
            if (a == 0) {
                return 0;
            }
    
            uint256 c = a * b;
            require(c / a == b, "SafeMath: multiplication overflow");
    
            return c;
        }
    
        /**
         * @dev Returns the integer division of two unsigned integers. Reverts on
         * division by zero. The result is rounded towards zero.
         *
         * Counterpart to Solidity's `/` operator. Note: this function uses a
         * `revert` opcode (which leaves remaining gas untouched) while Solidity
         * uses an invalid opcode to revert (consuming all remaining gas).
         *
         * Requirements:
         *
         * - The divisor cannot be zero.
         */
        function div(uint256 a, uint256 b) internal pure returns (uint256) {
            return div(a, b, "SafeMath: division by zero");
        }
    
        /**
         * @dev Returns the integer division of two unsigned integers. Reverts with custom message on
         * division by zero. The result is rounded towards zero.
         *
         * Counterpart to Solidity's `/` operator. Note: this function uses a
         * `revert` opcode (which leaves remaining gas untouched) while Solidity
         * uses an invalid opcode to revert (consuming all remaining gas).
         *
         * Requirements:
         *
         * - The divisor cannot be zero.
         */
        function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
            require(b > 0, errorMessage);
            uint256 c = a / b;
            // assert(a == b * c + a % b); // There is no case in which this doesn't hold
    
            return c;
        }
    
        /**
         * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
         * Reverts when dividing by zero.
         *
         * Counterpart to Solidity's `%` operator. This function uses a `revert`
         * opcode (which leaves remaining gas untouched) while Solidity uses an
         * invalid opcode to revert (consuming all remaining gas).
         *
         * Requirements:
         *
         * - The divisor cannot be zero.
         */
        function mod(uint256 a, uint256 b) internal pure returns (uint256) {
            return mod(a, b, "SafeMath: modulo by zero");
        }
    
        /**
         * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
         * Reverts with custom message when dividing by zero.
         *
         * Counterpart to Solidity's `%` operator. This function uses a `revert`
         * opcode (which leaves remaining gas untouched) while Solidity uses an
         * invalid opcode to revert (consuming all remaining gas).
         *
         * Requirements:
         *
         * - The divisor cannot be zero.
         */
        function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
            require(b != 0, errorMessage);
            return a % b;
        }
    }
function div(uint256 a, uint256 b) internal pure returns (uint256) {
    return div(a, b, "SafeMath: division by zero");
}

/**
 * @dev Returns the integer division of two unsigned integers. Reverts on
 * division by zero. The result is rounded towards zero.
 *
 * Counterpart to Solidity's `/` operator. Note: this function uses a
 * `revert` opcode (which leaves remaining gas untouched) while Solidity
 * uses an invalid opcode to revert (consuming all remaining gas).
 *
 * Requirements:
 *
 * - The divisor cannot be zero.
 */