library SafeMathInt {
int256 private constant MIN_INT256 = int256(1) << 255;
int256 private constant MAX_INT256 = ~(int256(1) << 255);

/**
* @dev Multiplies two int256 variables and fails on overflow.
*/
function mul(int256 a, int256 b) internal pure returns (int256) {
int256 c = a * b;

// Detect overflow when multiplying MIN_INT256 with -1
require(c != MIN_INT256 || (a & MIN_INT256) != (b & MIN_INT256));
require((b == 0) || (c / b == a));
return c;
}

/**
* @dev Division of two int256 variables and fails on overflow.
*/
function div(int256 a, int256 b) internal pure returns (int256) {
// Prevent overflow when dividing MIN_INT256 by -1
require(b != -1 || a != MIN_INT256);

// Solidity already throws when dividing by 0.
return a / b;
}

/**
* @dev Subtracts two int256 variables and fails on overflow.
*/
function sub(int256 a, int256 b) internal pure returns (int256) {
int256 c = a - b;
require((b >= 0 && c <= a) || (b < 0 && c > a));
return c;
}

/**
* @dev Adds two int256 variables and fails on overflow.
*/
function add(int256 a, int256 b) internal pure returns (int256) {
int256 c = a + b;
require((b >= 0 && c >= a) || (b < 0 && c < a));
return c;
}

/**
* @dev Converts to absolute value, and fails on overflow.
*/
function abs(int256 a) internal pure returns (int256) {
require(a != MIN_INT256);
return a < 0 ? -a : a;
}

function toUint256Safe(int256 a) internal pure returns (uint256) {
require(a >= 0);
return uint256(a);
}
}

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