// 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 BoringMath {
    function add(uint256 a, uint256 b) internal pure returns (uint256 c) {require((c = a + b) >= b, "BoringMath: Add Overflow");}
    function sub(uint256 a, uint256 b) internal pure returns (uint256 c) {require((c = a - b) <= a, "BoringMath: Underflow");}
    function mul(uint256 a, uint256 b) internal pure returns (uint256 c) {require(b == 0 || (c = a * b)/b == a, "BoringMath: Mul Overflow");}
    function to128(uint256 a) internal pure returns (uint128 c) {
        require(a <= uint128(-1), "BoringMath: uint128 Overflow");
        c = uint128(a);
    }
    function to64(uint256 a) internal pure returns (uint64 c) {
        require(a <= uint64(-1), "BoringMath: uint64 Overflow");
        c = uint64(a);
    }
    function to32(uint256 a) internal pure returns (uint32 c) {
        require(a <= uint32(-1), "BoringMath: uint32 Overflow");
        c = uint32(a);
    }
}
library BoringMath128 {
    function add(uint128 a, uint128 b) internal pure returns (uint128 c) {require((c = a + b) >= b, "BoringMath: Add Overflow");}
    function sub(uint128 a, uint128 b) internal pure returns (uint128 c) {require((c = a - b) <= a, "BoringMath: Underflow");}
}
library BoringMath64 {
    function add(uint64 a, uint64 b) internal pure returns (uint64 c) {require((c = a + b) >= b, "BoringMath: Add Overflow");}
    function sub(uint64 a, uint64 b) internal pure returns (uint64 c) {require((c = a - b) <= a, "BoringMath: Underflow");}
}
library BoringMath32 {
    function add(uint32 a, uint32 b) internal pure returns (uint32 c) {require((c = a + b) >= b, "BoringMath: Add Overflow");}
    function sub(uint32 a, uint32 b) internal pure returns (uint32 c) {require((c = a - b) <= a, "BoringMath: Underflow");}
}