library SafeMath {
    /*function add(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require((z = x + y) >= x, 'ds-math-add-overflow');
    }

    function sub(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require((z = x - y) <= x, 'ds-math-sub-underflow');
    }

    function mul(uint256 x, uint256 y) internal pure returns (uint256 z) {
        require(y == 0 || (z = x * y) / y == x, 'ds-math-mul-overflow');
    }*/

    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");
        return c;
    }

    function add(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, errorMessage);

        return c;
    }

    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        return sub(a, b, "SafeMath: subtraction underflow");
    }

    function sub(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b <= a, errorMessage);
        uint256 c = a - b;

        return c;
    }

    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;
    }

    function mul(uint256 a, uint256 b, string memory errorMessage) 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, errorMessage);

        return c;
    }

    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        return div(a, b, "SafeMath: division by zero");
    }

    function div(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        // Solidity only automatically asserts when dividing by 0
        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;
    }

    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        return mod(a, b, "SafeMath: modulo by zero");
    }

    function mod(uint256 a, uint256 b, string memory errorMessage) internal pure returns (uint256) {
        require(b != 0, errorMessage);
        return a % b;
    }
}
// a library for performing overflow-safe math, courtesy of DappHub (https://github.com/dapphub/ds-math)
function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a, "SafeMath: addition overflow");
        return c;
    }
/*function add(uint256 x, uint256 y) internal pure returns (uint256 z) {
 require((z = x + y) >= x, 'ds-math-add-overflow');
 }
 
 function sub(uint256 x, uint256 y) internal pure returns (uint256 z) {
 require((z = x - y) <= x, 'ds-math-sub-underflow');
 }
 
 function mul(uint256 x, uint256 y) internal pure returns (uint256 z) {
 require(y == 0 || (z = x * y) / y == x, 'ds-math-mul-overflow');
 }*/