library SafeMath {

    /**
     * @dev multiplies two unsigned integers, reverts on overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        // gas optimization: this is cheeper than requiring 'a' not being zero, but the
        // benefit is lost if 'b' is also tested.
        // see: https://github.com/OpenZeppelin/openzeppelin-solidity/pull/522
        if (a == 0) {
            return 0;
        }

        uint256 c = a * b;
        require(c / a == b, "safemath#mul: OVERFLOW");

        return c;
    }

    /**
     * @dev integer division of two unsigned integers truncating the quotient, reverts on division by zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        // solidity only automatically asserts when dividing by 0
        require(b > 0, "safemath#div: DIVISION_BY_ZERO");
        uint256 c = a / b;
        // assert(a == b * c + a % b); // there is no case in which this doesn't hold

        return c;
    }

    /**
     * @dev subtracts two unsigned integers, reverts on overflow (i.e. if subtrahend is greater than minuend).
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b <= a, "safemath#sub: UNDERFLOW");
        uint256 c = a - b;

        return c;
    }

    /**
     * @dev adds two unsigned integers, reverts on overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "safemath#add: OVERFLOW");

        return c;
    }

    /**
     * @dev divides two unsigned integers and returns the remainder (unsigned integer modulo),
     * reverts when dividing by zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b != 0, "safemath#mod: DIVISION_BY_ZERO");
        return a % b;
    }

}
/**
 * @title safemath
 * @dev unsigned math operations with safety checks that revert on error
 */
function div(uint256 a, uint256 b) internal pure returns (uint256) {
    // solidity only automatically asserts when dividing by 0
    require(b > 0, "safemath#div: DIVISION_BY_ZERO");
    uint256 c = a / b;
    // assert(a == b * c + a % b); // there is no case in which this doesn't hold

    return c;
}

/**
 * @dev integer division of two unsigned integers truncating the quotient, reverts on division by zero.
 */