library SafeMath32 {
  /**
    * @dev Returns the addition of two unsigned integers, reverting on
    * overflow.
    *
    * Counterpart to Solidity's `+` operator.
    *
    * Requirements:
    * - Addition cannot overflow.
    */
  function add(uint32 a, uint32 b) internal pure returns (uint32) {
    uint32 c = a + b;
    require(c >= a, "SafeMath: addition overflow");

    return c;
  }

  /**
    * @dev Returns the subtraction of two unsigned integers, reverting on
    * overflow (when the result is negative).
    *
    * Counterpart to Solidity's `-` operator.
    *
    * Requirements:
    * - Subtraction cannot overflow.
    */
  function sub(uint32 a, uint32 b) internal pure returns (uint32) {
    require(b <= a, "SafeMath: subtraction overflow");
    uint32 c = a - b;

    return c;
  }

  /**
    * @dev Returns the multiplication of two unsigned integers, reverting on
    * overflow.
    *
    * Counterpart to Solidity's `*` operator.
    *
    * Requirements:
    * - Multiplication cannot overflow.
    */
  function mul(uint32 a, uint32 b) internal pure returns (uint32) {
    // 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-solidity/pull/522
    if (a == 0) {
      return 0;
    }

    uint32 c = a * b;
    require(c / a == b, "SafeMath: multiplication overflow");

    return c;
  }

  /**
    * @dev Returns the integer division of two unsigned integers. Reverts on
    * division by zero. The result is rounded towards zero.
    *
    * Counterpart to Solidity's `/` operator. Note: this function uses a
    * `revert` opcode (which leaves remaining gas untouched) while Solidity
    * uses an invalid opcode to revert (consuming all remaining gas).
    *
    * Requirements:
    * - The divisor cannot be zero.
    */
  function div(uint32 a, uint32 b) internal pure returns (uint32) {
    // Solidity only automatically asserts when dividing by 0
    require(b > 0, "SafeMath: division by zero");
    uint32 c = a / b;
    // assert(a == b * c + a % b); // There is no case in which this doesn't hold

    return c;
  }

  /**
    * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
    * Reverts when dividing by zero.
    *
    * Counterpart to Solidity's `%` operator. This function uses a `revert`
    * opcode (which leaves remaining gas untouched) while Solidity uses an
    * invalid opcode to revert (consuming all remaining gas).
    *
    * Requirements:
    * - The divisor cannot be zero.
    */
  function mod(uint32 a, uint32 b) internal pure returns (uint32) {
    require(b != 0, "SafeMath: modulo by zero");
    return a % b;
  }
}
/**
 * @dev Wrappers over Solidity's arithmetic operations with added overflow
 * checks.
 *
 * Arithmetic operations in Solidity wrap on overflow. This can easily result
 * in bugs, because programmers usually assume that an overflow raises an
 * error, which is the standard behavior in high level programming languages.
 * `SafeMath` restores this intuition by reverting the transaction when an
 * operation overflows.
 *
 * Using this library instead of the unchecked operations eliminates an entire
 * class of bugs, so it's recommended to use it always.
 *
 * This library is a version of Open Zeppelin's SafeMath, modified to support
 * unsigned 32 bit integers.
 */
function mod(uint32 a, uint32 b) internal pure returns (uint32) {
  require(b != 0, "SafeMath: modulo by zero");
  return a % b;
}

/**
 * @dev Returns the remainder of dividing two unsigned integers. (unsigned integer modulo),
 * Reverts when dividing by zero.
 *
 * Counterpart to Solidity's `%` operator. This function uses a `revert`
 * opcode (which leaves remaining gas untouched) while Solidity uses an
 * invalid opcode to revert (consuming all remaining gas).
 *
 * Requirements:
 * - The divisor cannot be zero.
 */