// File: ERC20.sol



pragma solidity ^0.5.2;

import "./IERC20.sol";
import "./SafeMath.sol";

/**
 * @title Standard ERC20 token
 *
 * @dev Implementation of the basic standard token.
 * https://eips.ethereum.org/EIPS/eip-20
 * Originally based on code by FirstBlood:
 * https://github.com/Firstbloodio/token/blob/master/smart_contract/FirstBloodToken.sol
 *
 * This implementation emits additional Approval events, allowing applications to reconstruct the allowance status for
 * all accounts just by listening to said events. Note that this isn't required by the specification, and other
 * compliant implementations may not do it.
 */
contract ERC20 is IERC20 {
    using SafeMath for uint256;

    mapping (address => uint256) private _balances;

    mapping (address => mapping (address => uint256)) private _allowed;

    uint256 private _totalSupply;

    /**
     * @dev Total number of tokens in existence
     */
    function totalSupply() public view returns (uint256) {
        return _totalSupply;
    }

    /**
     * @dev Gets the balance of the specified address.
     * @param owner The address to query the balance of.
     * @return A uint256 representing the amount owned by the passed address.
     */
    function balanceOf(address owner) public view returns (uint256) {
        return _balances[owner];
    }

    /**
     * @dev Function to check the amount of tokens that an owner allowed to a spender.
     * @param owner address The address which owns the funds.
     * @param spender address The address which will spend the funds.
     * @return A uint256 specifying the amount of tokens still available for the spender.
     */
    function allowance(address owner, address spender) public view returns (uint256) {
        return _allowed[owner][spender];
    }

    /**
     * @dev Transfer token to a specified address
     * @param to The address to transfer to.
     * @param value The amount to be transferred.
     */
    function transfer(address to, uint256 value) public returns (bool) {
        _transfer(msg.sender, to, value);
        return true;
    }

    /**
     * @dev Approve the passed address to spend the specified amount of tokens on behalf of msg.sender.
     * Beware that changing an allowance with this method brings the risk that someone may use both the old
     * and the new allowance by unfortunate transaction ordering. One possible solution to mitigate this
     * race condition is to first reduce the spender's allowance to 0 and set the desired value afterwards:
     * https://github.com/ethereum/EIPs/issues/20#issuecomment-263524729
     * @param spender The address which will spend the funds.
     * @param value The amount of tokens to be spent.
     */
    function approve(address spender, uint256 value) public returns (bool) {
        _approve(msg.sender, spender, value);
        return true;
    }

    /**
     * @dev Transfer tokens from one address to another.
     * Note that while this function emits an Approval event, this is not required as per the specification,
     * and other compliant implementations may not emit the event.
     * @param from address The address which you want to send tokens from
     * @param to address The address which you want to transfer to
     * @param value uint256 the amount of tokens to be transferred
     */
    function transferFrom(address from, address to, uint256 value) public returns (bool) {
        _transfer(from, to, value);
        _approve(from, msg.sender, _allowed[from][msg.sender].sub(value));
        return true;
    }

    /**
     * @dev Increase the amount of tokens that an owner allowed to a spender.
     * approve should be called when _allowed[msg.sender][spender] == 0. To increment
     * allowed value is better to use this function to avoid 2 calls (and wait until
     * the first transaction is mined)
     * From MonolithDAO Token.sol
     * Emits an Approval event.
     * @param spender The address which will spend the funds.
     * @param addedValue The amount of tokens to increase the allowance by.
     */
    function increaseAllowance(address spender, uint256 addedValue) public returns (bool) {
        _approve(msg.sender, spender, _allowed[msg.sender][spender].add(addedValue));
        return true;
    }

    /**
     * @dev Decrease the amount of tokens that an owner allowed to a spender.
     * approve should be called when _allowed[msg.sender][spender] == 0. To decrement
     * allowed value is better to use this function to avoid 2 calls (and wait until
     * the first transaction is mined)
     * From MonolithDAO Token.sol
     * Emits an Approval event.
     * @param spender The address which will spend the funds.
     * @param subtractedValue The amount of tokens to decrease the allowance by.
     */
    function decreaseAllowance(address spender, uint256 subtractedValue) public returns (bool) {
        _approve(msg.sender, spender, _allowed[msg.sender][spender].sub(subtractedValue));
        return true;
    }

    /**
     * @dev Transfer token for a specified addresses
     * @param from The address to transfer from.
     * @param to The address to transfer to.
     * @param value The amount to be transferred.
     */
    function _transfer(address from, address to, uint256 value) internal {
        require(to != address(0));

        _balances[from] = _balances[from].sub(value);
        _balances[to] = _balances[to].add(value);
        emit Transfer(from, to, value);
    }

    /**
     * @dev Internal function that mints an amount of the token and assigns it to
     * an account. This encapsulates the modification of balances such that the
     * proper events are emitted.
     * @param account The account that will receive the created tokens.
     * @param value The amount that will be created.
     */
    function _mint(address account, uint256 value) internal {
        require(account != address(0));

        _totalSupply = _totalSupply.add(value);
        _balances[account] = _balances[account].add(value);
        emit Transfer(address(0), account, value);
    }

    /**
     * @dev Internal function that burns an amount of the token of a given
     * account.
     * @param account The account whose tokens will be burnt.
     * @param value The amount that will be burnt.
     */
    function _burn(address account, uint256 value) internal {
        require(account != address(0));

        _totalSupply = _totalSupply.sub(value);
        _balances[account] = _balances[account].sub(value);
        emit Transfer(account, address(0), value);
    }

    /**
     * @dev Approve an address to spend another addresses' tokens.
     * @param owner The address that owns the tokens.
     * @param spender The address that will spend the tokens.
     * @param value The number of tokens that can be spent.
     */
    function _approve(address owner, address spender, uint256 value) internal {
        require(spender != address(0));
        require(owner != address(0));

        _allowed[owner][spender] = value;
        emit Approval(owner, spender, value);
    }

    /**
     * @dev Internal function that burns an amount of the token of a given
     * account, deducting from the sender's allowance for said account. Uses the
     * internal burn function.
     * Emits an Approval event (reflecting the reduced allowance).
     * @param account The account whose tokens will be burnt.
     * @param value The amount that will be burnt.
     */
    function _burnFrom(address account, uint256 value) internal {
        _burn(account, value);
        _approve(account, msg.sender, _allowed[account][msg.sender].sub(value));
    }
}

// File: ERC20Burnable.sol



pragma solidity ^0.5.2;

import "./ERC20.sol";

/**
 * @title Burnable Token
 * @dev Token that can be irreversibly burned (destroyed).
 */
contract ERC20Burnable is ERC20 {
    /**
     * @dev Burns a specific amount of tokens.
     * @param value The amount of token to be burned.
     */
    function burn(uint256 value) public {
        _burn(msg.sender, value);
    }

    /**
     * @dev Burns a specific amount of tokens from the target address and decrements allowance
     * @param from address The account whose tokens will be burned.
     * @param value uint256 The amount of token to be burned.
     */
    function burnFrom(address from, uint256 value) public {
        _burnFrom(from, value);
    }
}

// File: ERC20Capped.sol



pragma solidity ^0.5.2;

import "./ERC20Mintable.sol";

/**
 * @title Capped token
 * @dev Mintable token with a token cap.
 */
contract ERC20Capped is ERC20Mintable {
    uint256 private _cap;

    constructor (uint256 cap) public {
        require(cap > 0);
        _cap = cap;
    }

    /**
     * @return the cap for the token minting.
     */
    function cap() public view returns (uint256) {
        return _cap;
    }

    function _mint(address account, uint256 value) internal {
        require(totalSupply().add(value) <= _cap);
        super._mint(account, value);
    }
}

// File: ERC20Detailed.sol



pragma solidity ^0.5.2;

import "./IERC20.sol";

/**
 * @title ERC20Detailed token
 * @dev The decimals are only for visualization purposes.
 * All the operations are done using the smallest and indivisible token unit,
 * just as on Ethereum all the operations are done in wei.
 */
contract ERC20Detailed is IERC20 {
    string private _name;
    string private _symbol;
    uint8 private _decimals;

    constructor (string memory name, string memory symbol, uint8 decimals) public {
        _name = name;
        _symbol = symbol;
        _decimals = decimals;
    }

    /**
     * @return the name of the token.
     */
    function name() public view returns (string memory) {
        return _name;
    }

    /**
     * @return the symbol of the token.
     */
    function symbol() public view returns (string memory) {
        return _symbol;
    }

    /**
     * @return the number of decimals of the token.
     */
    function decimals() public view returns (uint8) {
        return _decimals;
    }
}

// File: ERC20Mintable.sol



pragma solidity ^0.5.2;

import "./ERC20.sol";
import "./MinterRole.sol";

/**
 * @title ERC20Mintable
 * @dev ERC20 minting logic
 */
contract ERC20Mintable is ERC20, MinterRole {
    /**
     * @dev Function to mint tokens
     * @param to The address that will receive the minted tokens.
     * @param value The amount of tokens to mint.
     * @return A boolean that indicates if the operation was successful.
     */
    function mint(address to, uint256 value) public onlyMinter returns (bool) {
        _mint(to, value);
        return true;
    }
}

// File: ERC20Pausable.sol



pragma solidity ^0.5.2;

import "./ERC20.sol";
import "./Pausable.sol";

/**
 * @title Pausable token
 * @dev ERC20 modified with pausable transfers.
 */
contract ERC20Pausable is ERC20, Pausable {
    function transfer(address to, uint256 value) public whenNotPaused returns (bool) {
        return super.transfer(to, value);
    }

    function transferFrom(address from, address to, uint256 value) public whenNotPaused returns (bool) {
        return super.transferFrom(from, to, value);
    }

    function approve(address spender, uint256 value) public whenNotPaused returns (bool) {
        return super.approve(spender, value);
    }

    function increaseAllowance(address spender, uint addedValue) public whenNotPaused returns (bool success) {
        return super.increaseAllowance(spender, addedValue);
    }

    function decreaseAllowance(address spender, uint subtractedValue) public whenNotPaused returns (bool success) {
        return super.decreaseAllowance(spender, subtractedValue);
    }
}

// File: IERC20.sol



pragma solidity ^0.5.2;

/**
 * @title ERC20 interface
 * @dev see https://eips.ethereum.org/EIPS/eip-20
 */
interface IERC20 {
    function transfer(address to, uint256 value) external returns (bool);

    function approve(address spender, uint256 value) external returns (bool);

    function transferFrom(address from, address to, uint256 value) external returns (bool);

    function totalSupply() external view returns (uint256);

    function balanceOf(address who) external view returns (uint256);

    function allowance(address owner, address spender) external view returns (uint256);

    event Transfer(address indexed from, address indexed to, uint256 value);

    event Approval(address indexed owner, address indexed spender, uint256 value);
}

// File: MinterRole.sol



pragma solidity ^0.5.2;

import "./Roles.sol";

contract MinterRole {
    using Roles for Roles.Role;

    event MinterAdded(address indexed account);
    event MinterRemoved(address indexed account);

    Roles.Role private _minters;

    constructor () internal {
        _addMinter(msg.sender);
    }

    modifier onlyMinter() {
        require(isMinter(msg.sender));
        _;
    }

    function isMinter(address account) public view returns (bool) {
        return _minters.has(account);
    }

    function addMinter(address account) public onlyMinter {
        _addMinter(account);
    }

    function renounceMinter() public {
        _removeMinter(msg.sender);
    }

    function _addMinter(address account) internal {
        _minters.add(account);
        emit MinterAdded(account);
    }

    function _removeMinter(address account) internal {
        _minters.remove(account);
        emit MinterRemoved(account);
    }
}

// File: Ownable.sol



pragma solidity ^0.5.2;

/**
 * @title Ownable
 * @dev The Ownable contract has an owner address, and provides basic authorization control
 * functions, this simplifies the implementation of "user permissions".
 */
contract Ownable {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev The Ownable constructor sets the original `owner` of the contract to the sender
     * account.
     */
    constructor () internal {
        _owner = msg.sender;
        emit OwnershipTransferred(address(0), _owner);
    }

    /**
     * @return the address of the owner.
     */
    function owner() public view returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        require(isOwner());
        _;
    }

    /**
     * @return true if `msg.sender` is the owner of the contract.
     */
    function isOwner() public view returns (bool) {
        return msg.sender == _owner;
    }

    /**
     * @dev Allows the current owner to relinquish control of the contract.
     * It will not be possible to call the functions with the `onlyOwner`
     * modifier anymore.
     * @notice Renouncing ownership will leave the contract without an owner,
     * thereby removing any functionality that is only available to the owner.
     */
    function renounceOwnership() public onlyOwner {
        emit OwnershipTransferred(_owner, address(0));
        _owner = address(0);
    }

    /**
     * @dev Allows the current owner to transfer control of the contract to a newOwner.
     * @param newOwner The address to transfer ownership to.
     */
    function transferOwnership(address newOwner) public onlyOwner {
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers control of the contract to a newOwner.
     * @param newOwner The address to transfer ownership to.
     */
    function _transferOwnership(address newOwner) internal {
        require(newOwner != address(0));
        emit OwnershipTransferred(_owner, newOwner);
        _owner = newOwner;
    }
}

// File: Pausable.sol



pragma solidity ^0.5.2;

import "./PauserRole.sol";

/**
 * @title Pausable
 * @dev Base contract which allows children to implement an emergency stop mechanism.
 */
contract Pausable is PauserRole {
    event Paused(address account);
    event Unpaused(address account);

    bool private _paused;

    constructor () internal {
        _paused = false;
    }

    /**
     * @return true if the contract is paused, false otherwise.
     */
    function paused() public view returns (bool) {
        return _paused;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is not paused.
     */
    modifier whenNotPaused() {
        require(!_paused);
        _;
    }

    /**
     * @dev Modifier to make a function callable only when the contract is paused.
     */
    modifier whenPaused() {
        require(_paused);
        _;
    }

    /**
     * @dev called by the owner to pause, triggers stopped state
     */
    function pause() public onlyPauser whenNotPaused {
        _paused = true;
        emit Paused(msg.sender);
    }

    /**
     * @dev called by the owner to unpause, returns to normal state
     */
    function unpause() public onlyPauser whenPaused {
        _paused = false;
        emit Unpaused(msg.sender);
    }
}

// File: PauserRole.sol



pragma solidity ^0.5.2;

import "./Roles.sol";

contract PauserRole {
    using Roles for Roles.Role;

    event PauserAdded(address indexed account);
    event PauserRemoved(address indexed account);

    Roles.Role private _pausers;

    constructor () internal {
        _addPauser(msg.sender);
    }

    modifier onlyPauser() {
        require(isPauser(msg.sender));
        _;
    }

    function isPauser(address account) public view returns (bool) {
        return _pausers.has(account);
    }

    function addPauser(address account) public onlyPauser {
        _addPauser(account);
    }

    function renouncePauser() public {
        _removePauser(msg.sender);
    }

    function _addPauser(address account) internal {
        _pausers.add(account);
        emit PauserAdded(account);
    }

    function _removePauser(address account) internal {
        _pausers.remove(account);
        emit PauserRemoved(account);
    }
}

// File: RaeMintContract.sol



pragma solidity 0.5.7;

import "./RaeToken.sol";
import "Ownable.sol";

contract RaeMintContract is Ownable {
    using SafeMath for uint256;

    RaeToken private _token;
    uint256 constant _pct = 28;

    
    
    /**
    * @dev create minting contract, passing token contract that will be the target of minting.
    * On deployment, deployer of RaeToken contract will be given minterRole. With that minterRole the deployer will
    * assign minterRole to this contract, and finally the deployer will revoke minterRole from himself so 
    * that this contract is the only possible minter for RaeToken. Owner of this contract will be the only person
    * who can issue mint, bulkMint functions
     */
    constructor(RaeToken token) Ownable() public 
    {
        _token = token;
    }

    /**
    * @dev perform a bulk mint, only callable by addresses that have mintRole. aggregators[i] will be minted _pct * values[i] and
    * addresses[i] will be minted values[i] - pct * values[i]
    * Will revert if:
    * addresses.length <= 0
    * the adresses.length != values.length or addresses.length != aggregators.length
    * totalSent != _mintAmount

    * @param addresses array of addresses where amount minted to addresses[i] is values[i] - _pct * values[i]
    * @param values array of mint values
    * @param aggregators array of addresses where amount minted to aggregators[i] is _pct * values[i]
    * @return A boolean that indicates the operation was successful
     */
    function bulkMintAggregator(address[] memory addresses, uint256[] memory values, address[] memory aggregators) public onlyOwner returns (bool)
    {
        if(_token.period() != 0)
        {
            uint256 totalSent = 0;
            require(addresses.length > 0);
            require(addresses.length == values.length);
            require(addresses.length == aggregators.length);

            uint256 addrSize = addresses.length;
            uint256 size = addrSize.add(addrSize);
            address[] memory bulkAddresses = new address[](size);
            uint256[] memory bulkValues = new uint256[](size);

            uint256 j = 0;
            for(uint256 i = 0; i < addresses.length; ++i)
            {
                uint256 aggregatorReward = values[i].mul(_pct).div(100);
                uint256 creatorReward = values[i].sub(aggregatorReward);
                totalSent = totalSent.add(aggregatorReward + creatorReward);
                
                // add address[i] and aggregators[i] to bulkAddresses
                bulkAddresses[j] = addresses[i];
                bulkValues[j] = creatorReward;

                bulkAddresses[j+1] = aggregators[i];
                bulkValues[j+1] = aggregatorReward;

                // increment j by 2
                j = j + 2;
            }
            require(totalSent <= _token.remainingInPeriod());
            _token.mintBulk(bulkAddresses, bulkValues); // perform the mint or parts of mint for this period       
            return true;
        }
        else 
        {
            _bulkMintFirstPeriod(addresses, values);
            return true;
        }
    }

    /**
    @dev function can only only be called when token mint period is 0, this is to handle the first minting period gracefully, without burning extra tokens
     */
    function _bulkMintFirstPeriod(address[] memory addresses, uint256[] memory values) internal returns (bool) {
        require(_token.period() == 0);
        require(addresses.length != 0);
        require(addresses.length == values.length);

        uint256 totalSent = 0;
        for(uint256 i =0; i < addresses.length; ++i) totalSent = totalSent.add(values[i]);
        require(totalSent <= _token.remainingInPeriod());
        _token.mintBulk(addresses, values);
        return true;
    }



     /**
     * @dev function addMinter should be used if switching minting contracts. Minting contracts will be switched
     * in the future to include a sufficient reward to incentivize federated servers to work for the network. 
     * This amount will be determined after the costs of running federated servers are known after 
     * a period of initial network usage. 
     * Decision was made to switch contracts rather than use malleable variables for transparency 
     * First add address of new minting contract as minter, then renounce
     * mintingRole for this contract, making it unable to mint
     */ 
    function addMinter(address addr) external onlyOwner returns (bool)
    {
        _token.addMinter(addr);
        return true;
    }

    /**
     * @dev renounce minting role from this smart contract, should be used if switching minting contracts
     */
    function renounceMintingRole() external onlyOwner returns (bool)
    {
        _token.renounceMinter();
        return true;
    }

    
    function period() external view returns (uint256){
        return _token.period();
    }

    function mintAmount() external view returns (uint256){
        return _token.mintAmount();
    }


    function tokensRemainingInPeriod() external view returns (uint256) {
        return _token.remainingInPeriod();
    }

    function tokensInPeriod() external view returns (uint256) {
        return _token.totalInPeriod();
    }

    /**
    @dev get the token contract's address to which this contract is issuing minting calls
    @return address of token contract
     */
    function token() external view returns (address)
    {
        return address(_token);
    }


    

    


}
// File: RaeToken.sol



pragma solidity 0.5.7;

import "./ERC20Detailed.sol";
import "./ERC20Burnable.sol";
import "./ERC20Capped.sol";
import "./ERC20Pausable.sol";


/**
@dev RaeToken Contract
requirements:
 - address that deployed RaeToken can pause contract and release pauseRole in future
 - address that deployed RaeToken has mintRole and can release mintRole in future
 - RaeMintContract has mintRole after deployment
 - totalSupply is capped at 34 million RAE = 34000000 RAE, or 34000000e18 ROK (1 RAE = 1e18 ROK)
 - every 1700 _mintPeriods _mintAmount is halved
 - _mintAmount starts at 10000 RAE = 10000e18 ROK
 - halveEvery can never be changed
 */
contract RaeToken is ERC20Detailed, ERC20Capped, ERC20Burnable, ERC20Pausable {
    uint256 private _mintAmount = 216000e18;
    uint256 private _mintPeriods = 0;
    uint256 private _totalInPeriod = 0;
    uint256 constant private _halveEvery = 1700; // halve mint amount every 1700 mint periods
    mapping (address => uint256) private _balances;

    constructor(string memory name, string memory symbol, uint8 decimals, uint256 cap)
        ERC20Burnable()
        ERC20Mintable()
        ERC20Capped(cap)
        ERC20Detailed(name, symbol, decimals)
        ERC20Pausable()
        ERC20()
    public 
    {
        _mint(msg.sender, 84000e18);
    }

    /**
    * @dev perform a minting period
    * requirements:
    * - addresses.length == values.length != 0
    * - only addresses with minter role should be able to call this function
    * - totalSent == _mintAmount
    * - every time this function returns successfully (true) _mintPeriods is incremented by 1
    * - every 1700 _mintPeriods _mintAmount is halved. e.g. when _mintPeriods = 1700 then _mintAmount = 5000e18
    * - addresses[i] is minted values[i], accepatable to have duplicate addresses
    @param addresses array of addresses where amount minted to addresses[i] is values[i]
    @param values array of token amounts that add up to _mintAmount
     */
    function mintBulk(address[] calldata addresses, uint256[] calldata values) external whenNotPaused onlyMinter returns (bool) {
        
        require(addresses.length > 0);
        require(addresses.length == values.length);

        for(uint256 i = 0; i < addresses.length; ++i) {
            _totalInPeriod = _totalInPeriod.add(values[i]);
            _mint(addresses[i], values[i]);
        }
        require(_totalInPeriod <= _mintAmount);
        if( _totalInPeriod == _mintAmount) _updateMintParams();

        return true;
    }


    function period() external view returns (uint256){
        return _mintPeriods;
    }

    function mintAmount() external view returns (uint256){
        return _mintAmount;
    }

    function _updateMintParams() internal returns (bool) {
        // first period is for 216,000 RAE, after this will go to 10000 RAE until decay
        if(_mintPeriods == 0) _mintAmount = 10000e18;

        // increment period
        _mintPeriods = _mintPeriods.add(1);

        // decay if _mintPeriods is 1700, 3400, 5100, etc. Target for 1 mint per day
        if(_mintPeriods % _halveEvery == 0) _mintAmount = _mintAmount.div(2);

        // reset the _totalInPeriod to 0
        _totalInPeriod = 0;

        return true;
    }

    function remainingInPeriod() external view returns (uint256) {
        return _mintAmount - _totalInPeriod;
    }

    function totalInPeriod() external view returns (uint256) {
        return _totalInPeriod;
    }

    /**
    @dev do not allow mint during pause
     */
    function mint(address to, uint256 value) public whenNotPaused onlyMinter returns (bool) {
        //super.mint(to, value);
        revert();
    }

    /**
    @dev do not allow burn during pause
     */
    function burn(uint256 value) public whenNotPaused {
        super.burn(value);
    }

    function burnFrom(address from, uint256 value) public whenNotPaused {
        super.burnFrom(from, value);
    }

}
// File: Roles.sol



pragma solidity ^0.5.2;

/**
 * @title Roles
 * @dev Library for managing addresses assigned to a Role.
 */
library Roles {
    struct Role {
        mapping (address => bool) bearer;
    }

    /**
     * @dev give an account access to this role
     */
    function add(Role storage role, address account) internal {
        require(account != address(0));
        require(!has(role, account));

        role.bearer[account] = true;
    }

    /**
     * @dev remove an account's access to this role
     */
    function remove(Role storage role, address account) internal {
        require(account != address(0));
        require(has(role, account));

        role.bearer[account] = false;
    }

    /**
     * @dev check if an account has this role
     * @return bool
     */
    function has(Role storage role, address account) internal view returns (bool) {
        require(account != address(0));
        return role.bearer[account];
    }
}

// File: SafeMath.sol



pragma solidity ^0.5.2;

/**
 * @title SafeMath
 * @dev Unsigned math operations with safety checks that revert on error
 */
library SafeMath {
    /**
     * @dev Multiplies two unsigned integers, reverts on overflow.
     */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        // 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;
        }

        uint256 c = a * b;
        require(c / a == b);

        return c;
    }

    /**
     * @dev Integer division of two unsigned integers truncating the quotient, reverts on division by zero.
     */
    function div(uint256 a, uint256 b) internal pure returns (uint256) {
        // Solidity only automatically asserts when dividing by 0
        require(b > 0);
        uint256 c = a / b;
        // assert(a == b * c + a % b); // There is no case in which this doesn't hold

        return c;
    }

    /**
     * @dev Subtracts two unsigned integers, reverts on overflow (i.e. if subtrahend is greater than minuend).
     */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b <= a);
        uint256 c = a - b;

        return c;
    }

    /**
     * @dev Adds two unsigned integers, reverts on overflow.
     */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        require(c >= a);

        return c;
    }

    /**
     * @dev Divides two unsigned integers and returns the remainder (unsigned integer modulo),
     * reverts when dividing by zero.
     */
    function mod(uint256 a, uint256 b) internal pure returns (uint256) {
        require(b != 0);
        return a % b;
    }
}