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pragma solidity ^0.4.15;
// ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
/**
 * @title SafeMath
 * @dev Math operations with safety checks that throw on error
 */
library SafeMath {
  function mul(uint256 a, uint256 b) internal constant returns (uint256) {
    uint256 c = a * b;
    assert(a == 0 || c / a == b);
    return c;
  }
  function div(uint256 a, uint256 b) internal constant returns (uint256) {
    // assert(b > 0); // Solidity automatically throws when dividing by 0
    uint256 c = a / b;
    // assert(a == b * c + a % b); // There is no case in which this doesn't hold
    return c;
  }
  function sub(uint256 a, uint256 b) internal constant returns (uint256) {
    assert(b <= a);
    return a - b;
  }
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