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

return c;
}

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

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 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) {
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;
}
}

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