// SPDX-License-Identifier: MIT
pragma solidity 0.6.12;

// a library for performing overflow-safe math, updated with awesomeness from of DappHub (https://github.com/dapphub/ds-math)
library SafeMath {
    function add(uint256 a, uint256 b) internal pure returns (uint256 c) {
        require((c = a + b) >= b, "SafeMath: Add Overflow");
    }

    function sub(uint256 a, uint256 b) internal pure returns (uint256 c) {
        require((c = a - b) <= a, "SafeMath: Underflow");
    }

    function mul(uint256 a, uint256 b) internal pure returns (uint256 c) {
        require(b == 0 || (c = a * b) / b == a, "SafeMath: Mul Overflow");
    }

    function div(uint256 a, uint256 b) internal pure returns (uint256 c) {
        require(b > 0, "SafeMath: Div by Zero");
        c = a / b;
    }

    function to128(uint256 a) internal pure returns (uint128 c) {
        require(a <= uint128(-1), "SafeMath: uint128 Overflow");
        c = uint128(a);
    }
}

library SafeMath128 {
    function add(uint128 a, uint128 b) internal pure returns (uint128 c) {
        require((c = a + b) >= b, "SafeMath: Add Overflow");
    }

    function sub(uint128 a, uint128 b) internal pure returns (uint128 c) {
        require((c = a - b) <= a, "SafeMath: Underflow");
    }
}