// File: Address.sol



pragma solidity ^0.5.0;

/**
 * Utility library of inline functions on addresses
 */
library Address {
    /**
     * Returns whether the target address is a contract
     * @dev This function will return false if invoked during the constructor of a contract,
     * as the code is not actually created until after the constructor finishes.
     * @param account address of the account to check
     * @return whether the target address is a contract
     */
    function isContract(address account) internal view returns (bool) {
        uint256 size;
        // XXX Currently there is no better way to check if there is a contract in an address
        // than to check the size of the code at that address.
        // See https://ethereum.stackexchange.com/a/14016/36603
        // for more details about how this works.
        // TODO Check this again before the Serenity release, because all addresses will be
        // contracts then.
        // solhint-disable-next-line no-inline-assembly
        assembly { size := extcodesize(account) }
        return size > 0;
    }
}

// File: BaseRegistrar.sol



pragma solidity >=0.4.24;

import "./ENS.sol";
import "./IERC721.sol";
import "./Ownable.sol";

contract BaseRegistrar is IERC721, Ownable {
    uint constant public GRACE_PERIOD = 90 days;

    event ControllerAdded(address indexed controller);
    event ControllerRemoved(address indexed controller);
    event NameMigrated(uint256 indexed id, address indexed owner, uint expires);
    event NameRegistered(uint256 indexed id, address indexed owner, uint expires);
    event NameRenewed(uint256 indexed id, uint expires);

    // The ENS registry
    ENS public ens;

    // The namehash of the TLD this registrar owns (eg, .eth)
    bytes32 public baseNode;

    // A map of addresses that are authorised to register and renew names.
    mapping(address=>bool) public controllers;

    // Authorises a controller, who can register and renew domains.
    function addController(address controller) external;

    // Revoke controller permission for an address.
    function removeController(address controller) external;

    // Set the resolver for the TLD this registrar manages.
    function setResolver(address resolver) external;

    // Returns the expiration timestamp of the specified label hash.
    function nameExpires(uint256 id) external view returns(uint);

    // Returns true iff the specified name is available for registration.
    function available(uint256 id) public view returns(bool);

    /**
     * @dev Register a name.
     */
    function register(uint256 id, address owner, uint duration) external returns(uint);

    function renew(uint256 id, uint duration) external returns(uint);

    /**
     * @dev Reclaim ownership of a name in ENS, if you own it in the registrar.
     */
    function reclaim(uint256 id, address owner) external;
}
// File: BaseRegistrarImplementation.sol



pragma solidity ^0.5.0;

import "./ENS.sol";
import "./ERC721.sol";
import "./BaseRegistrar.sol";

contract BaseRegistrarImplementation is BaseRegistrar, ERC721 {
    // A map of expiry times
    mapping(uint256=>uint) expiries;

    bytes4 constant private INTERFACE_META_ID = bytes4(keccak256("supportsInterface(bytes4)"));
    bytes4 constant private ERC721_ID = bytes4(
        keccak256("balanceOf(address)") ^
        keccak256("ownerOf(uint256)") ^
        keccak256("approve(address,uint256)") ^
        keccak256("getApproved(uint256)") ^
        keccak256("setApprovalForAll(address,bool)") ^
        keccak256("isApprovedForAll(address,address)") ^
        keccak256("transferFrom(address,address,uint256)") ^
        keccak256("safeTransferFrom(address,address,uint256)") ^
        keccak256("safeTransferFrom(address,address,uint256,bytes)")
    );
    bytes4 constant private RECLAIM_ID = bytes4(keccak256("reclaim(uint256,address)"));

    constructor(ENS _ens, bytes32 _baseNode) public {
        ens = _ens;
        baseNode = _baseNode;
    }

    modifier live {
        require(ens.owner(baseNode) == address(this));
        _;
    }

    modifier onlyController {
        require(controllers[msg.sender]);
        _;
    }

    /**
     * @dev Gets the owner of the specified token ID. Names become unowned
     *      when their registration expires.
     * @param tokenId uint256 ID of the token to query the owner of
     * @return address currently marked as the owner of the given token ID
     */
    function ownerOf(uint256 tokenId) public view returns (address) {
        require(expiries[tokenId] > now);
        return super.ownerOf(tokenId);
    }

    // Authorises a controller, who can register and renew domains.
    function addController(address controller) external onlyOwner {
        controllers[controller] = true;
        emit ControllerAdded(controller);
    }

    // Revoke controller permission for an address.
    function removeController(address controller) external onlyOwner {
        controllers[controller] = false;
        emit ControllerRemoved(controller);
    }

    // Set the resolver for the TLD this registrar manages.
    function setResolver(address resolver) external onlyOwner {
        ens.setResolver(baseNode, resolver);
    }

    // Returns the expiration timestamp of the specified id.
    function nameExpires(uint256 id) external view returns(uint) {
        return expiries[id];
    }

    // Returns true iff the specified name is available for registration.
    function available(uint256 id) public view returns(bool) {
        // Not available if it's registered here or in its grace period.
        return expiries[id] + GRACE_PERIOD < now;
    }

    /**
     * @dev Register a name.
     * @param id The token ID (keccak256 of the label).
     * @param owner The address that should own the registration.
     * @param duration Duration in seconds for the registration.
     */
    function register(uint256 id, address owner, uint duration) external returns(uint) {
      return _register(id, owner, duration, true);
    }

    /**
     * @dev Register a name, without modifying the registry.
     * @param id The token ID (keccak256 of the label).
     * @param owner The address that should own the registration.
     * @param duration Duration in seconds for the registration.
     */
    function registerOnly(uint256 id, address owner, uint duration) external returns(uint) {
      return _register(id, owner, duration, false);
    }

    function _register(uint256 id, address owner, uint duration, bool updateRegistry) internal live onlyController returns(uint) {
        require(available(id));
        require(now + duration + GRACE_PERIOD > now + GRACE_PERIOD); // Prevent future overflow

        expiries[id] = now + duration;
        if(_exists(id)) {
            // Name was previously owned, and expired
            _burn(id);
        }
        _mint(owner, id);
        if(updateRegistry) {
            ens.setSubnodeOwner(baseNode, bytes32(id), owner);
        }

        emit NameRegistered(id, owner, now + duration);

        return now + duration;
    }

    function renew(uint256 id, uint duration) external live onlyController returns(uint) {
        require(expiries[id] + GRACE_PERIOD >= now); // Name must be registered here or in grace period
        require(expiries[id] + duration + GRACE_PERIOD > duration + GRACE_PERIOD); // Prevent future overflow

        expiries[id] += duration;
        emit NameRenewed(id, expiries[id]);
        return expiries[id];
    }

    /**
     * @dev Reclaim ownership of a name in ENS, if you own it in the registrar.
     */
    function reclaim(uint256 id, address owner) external live {
        require(_isApprovedOrOwner(msg.sender, id));
        ens.setSubnodeOwner(baseNode, bytes32(id), owner);
    }

    function supportsInterface(bytes4 interfaceID) external view returns (bool) {
        return interfaceID == INTERFACE_META_ID ||
               interfaceID == ERC721_ID ||
               interfaceID == RECLAIM_ID;
    }
}
// File: ENS.sol



pragma solidity >=0.4.24;

interface ENS {

    // Logged when the owner of a node assigns a new owner to a subnode.
    event NewOwner(bytes32 indexed node, bytes32 indexed label, address owner);

    // Logged when the owner of a node transfers ownership to a new account.
    event Transfer(bytes32 indexed node, address owner);

    // Logged when the resolver for a node changes.
    event NewResolver(bytes32 indexed node, address resolver);

    // Logged when the TTL of a node changes
    event NewTTL(bytes32 indexed node, uint64 ttl);

    // Logged when an operator is added or removed.
    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    function setRecord(bytes32 node, address owner, address resolver, uint64 ttl) external;
    function setSubnodeRecord(bytes32 node, bytes32 label, address owner, address resolver, uint64 ttl) external;
    function setSubnodeOwner(bytes32 node, bytes32 label, address owner) external returns(bytes32);
    function setResolver(bytes32 node, address resolver) external;
    function setOwner(bytes32 node, address owner) external;
    function setTTL(bytes32 node, uint64 ttl) external;
    function setApprovalForAll(address operator, bool approved) external;
    function owner(bytes32 node) external view returns (address);
    function resolver(bytes32 node) external view returns (address);
    function ttl(bytes32 node) external view returns (uint64);
    function recordExists(bytes32 node) external view returns (bool);
    function isApprovedForAll(address owner, address operator) external view returns (bool);
}

// File: ERC165.sol



pragma solidity ^0.5.0;

import "./IERC165.sol";

/**
 * @title ERC165
 * @author Matt Condon (@shrugs)
 * @dev Implements ERC165 using a lookup table.
 */
contract ERC165 is IERC165 {
    bytes4 private constant _INTERFACE_ID_ERC165 = 0x01ffc9a7;
    /**
     * 0x01ffc9a7 ===
     *     bytes4(keccak256('supportsInterface(bytes4)'))
     */

    /**
     * @dev a mapping of interface id to whether or not it's supported
     */
    mapping(bytes4 => bool) private _supportedInterfaces;

    /**
     * @dev A contract implementing SupportsInterfaceWithLookup
     * implement ERC165 itself
     */
    constructor () internal {
        _registerInterface(_INTERFACE_ID_ERC165);
    }

    /**
     * @dev implement supportsInterface(bytes4) using a lookup table
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool) {
        return _supportedInterfaces[interfaceId];
    }

    /**
     * @dev internal method for registering an interface
     */
    function _registerInterface(bytes4 interfaceId) internal {
        require(interfaceId != 0xffffffff);
        _supportedInterfaces[interfaceId] = true;
    }
}

// File: ERC721.sol



pragma solidity ^0.5.0;

import "./IERC721.sol";
import "./IERC721Receiver.sol";
import "./SafeMath.sol";
import "./Address.sol";
import "./ERC165.sol";

/**
 * @title ERC721 Non-Fungible Token Standard basic implementation
 * @dev see https://github.com/ethereum/EIPs/blob/master/EIPS/eip-721.md
 */
contract ERC721 is ERC165, IERC721 {
    using SafeMath for uint256;
    using Address for address;

    // Equals to `bytes4(keccak256("onERC721Received(address,address,uint256,bytes)"))`
    // which can be also obtained as `IERC721Receiver(0).onERC721Received.selector`
    bytes4 private constant _ERC721_RECEIVED = 0x150b7a02;

    // Mapping from token ID to owner
    mapping (uint256 => address) private _tokenOwner;

    // Mapping from token ID to approved address
    mapping (uint256 => address) private _tokenApprovals;

    // Mapping from owner to number of owned token
    mapping (address => uint256) private _ownedTokensCount;

    // Mapping from owner to operator approvals
    mapping (address => mapping (address => bool)) private _operatorApprovals;

    bytes4 private constant _INTERFACE_ID_ERC721 = 0x80ac58cd;
    /*
     * 0x80ac58cd ===
     *     bytes4(keccak256('balanceOf(address)')) ^
     *     bytes4(keccak256('ownerOf(uint256)')) ^
     *     bytes4(keccak256('approve(address,uint256)')) ^
     *     bytes4(keccak256('getApproved(uint256)')) ^
     *     bytes4(keccak256('setApprovalForAll(address,bool)')) ^
     *     bytes4(keccak256('isApprovedForAll(address,address)')) ^
     *     bytes4(keccak256('transferFrom(address,address,uint256)')) ^
     *     bytes4(keccak256('safeTransferFrom(address,address,uint256)')) ^
     *     bytes4(keccak256('safeTransferFrom(address,address,uint256,bytes)'))
     */

    constructor () public {
        // register the supported interfaces to conform to ERC721 via ERC165
        _registerInterface(_INTERFACE_ID_ERC721);
    }

    /**
     * @dev Gets the balance of the specified address
     * @param owner address to query the balance of
     * @return uint256 representing the amount owned by the passed address
     */
    function balanceOf(address owner) public view returns (uint256) {
        require(owner != address(0));
        return _ownedTokensCount[owner];
    }

    /**
     * @dev Gets the owner of the specified token ID
     * @param tokenId uint256 ID of the token to query the owner of
     * @return owner address currently marked as the owner of the given token ID
     */
    function ownerOf(uint256 tokenId) public view returns (address) {
        address owner = _tokenOwner[tokenId];
        require(owner != address(0));
        return owner;
    }

    /**
     * @dev Approves another address to transfer the given token ID
     * The zero address indicates there is no approved address.
     * There can only be one approved address per token at a given time.
     * Can only be called by the token owner or an approved operator.
     * @param to address to be approved for the given token ID
     * @param tokenId uint256 ID of the token to be approved
     */
    function approve(address to, uint256 tokenId) public {
        address owner = ownerOf(tokenId);
        require(to != owner);
        require(msg.sender == owner || isApprovedForAll(owner, msg.sender));

        _tokenApprovals[tokenId] = to;
        emit Approval(owner, to, tokenId);
    }

    /**
     * @dev Gets the approved address for a token ID, or zero if no address set
     * Reverts if the token ID does not exist.
     * @param tokenId uint256 ID of the token to query the approval of
     * @return address currently approved for the given token ID
     */
    function getApproved(uint256 tokenId) public view returns (address) {
        require(_exists(tokenId));
        return _tokenApprovals[tokenId];
    }

    /**
     * @dev Sets or unsets the approval of a given operator
     * An operator is allowed to transfer all tokens of the sender on their behalf
     * @param to operator address to set the approval
     * @param approved representing the status of the approval to be set
     */
    function setApprovalForAll(address to, bool approved) public {
        require(to != msg.sender);
        _operatorApprovals[msg.sender][to] = approved;
        emit ApprovalForAll(msg.sender, to, approved);
    }

    /**
     * @dev Tells whether an operator is approved by a given owner
     * @param owner owner address which you want to query the approval of
     * @param operator operator address which you want to query the approval of
     * @return bool whether the given operator is approved by the given owner
     */
    function isApprovedForAll(address owner, address operator) public view returns (bool) {
        return _operatorApprovals[owner][operator];
    }

    /**
     * @dev Transfers the ownership of a given token ID to another address
     * Usage of this method is discouraged, use `safeTransferFrom` whenever possible
     * Requires the msg sender to be the owner, approved, or operator
     * @param from current owner of the token
     * @param to address to receive the ownership of the given token ID
     * @param tokenId uint256 ID of the token to be transferred
    */
    function transferFrom(address from, address to, uint256 tokenId) public {
        require(_isApprovedOrOwner(msg.sender, tokenId));

        _transferFrom(from, to, tokenId);
    }

    /**
     * @dev Safely transfers the ownership of a given token ID to another address
     * If the target address is a contract, it must implement `onERC721Received`,
     * which is called upon a safe transfer, and return the magic value
     * `bytes4(keccak256("onERC721Received(address,address,uint256,bytes)"))`; otherwise,
     * the transfer is reverted.
     *
     * Requires the msg sender to be the owner, approved, or operator
     * @param from current owner of the token
     * @param to address to receive the ownership of the given token ID
     * @param tokenId uint256 ID of the token to be transferred
    */
    function safeTransferFrom(address from, address to, uint256 tokenId) public {
        safeTransferFrom(from, to, tokenId, "");
    }

    /**
     * @dev Safely transfers the ownership of a given token ID to another address
     * If the target address is a contract, it must implement `onERC721Received`,
     * which is called upon a safe transfer, and return the magic value
     * `bytes4(keccak256("onERC721Received(address,address,uint256,bytes)"))`; otherwise,
     * the transfer is reverted.
     * Requires the msg sender to be the owner, approved, or operator
     * @param from current owner of the token
     * @param to address to receive the ownership of the given token ID
     * @param tokenId uint256 ID of the token to be transferred
     * @param _data bytes data to send along with a safe transfer check
     */
    function safeTransferFrom(address from, address to, uint256 tokenId, bytes memory _data) public {
        transferFrom(from, to, tokenId);
        require(_checkOnERC721Received(from, to, tokenId, _data));
    }

    /**
     * @dev Returns whether the specified token exists
     * @param tokenId uint256 ID of the token to query the existence of
     * @return whether the token exists
     */
    function _exists(uint256 tokenId) internal view returns (bool) {
        address owner = _tokenOwner[tokenId];
        return owner != address(0);
    }

    /**
     * @dev Returns whether the given spender can transfer a given token ID
     * @param spender address of the spender to query
     * @param tokenId uint256 ID of the token to be transferred
     * @return bool whether the msg.sender is approved for the given token ID,
     *    is an operator of the owner, or is the owner of the token
     */
    function _isApprovedOrOwner(address spender, uint256 tokenId) internal view returns (bool) {
        address owner = ownerOf(tokenId);
        return (spender == owner || getApproved(tokenId) == spender || isApprovedForAll(owner, spender));
    }

    /**
     * @dev Internal function to mint a new token
     * Reverts if the given token ID already exists
     * @param to The address that will own the minted token
     * @param tokenId uint256 ID of the token to be minted
     */
    function _mint(address to, uint256 tokenId) internal {
        require(to != address(0));
        require(!_exists(tokenId));

        _tokenOwner[tokenId] = to;
        _ownedTokensCount[to] = _ownedTokensCount[to].add(1);

        emit Transfer(address(0), to, tokenId);
    }

    /**
     * @dev Internal function to burn a specific token
     * Reverts if the token does not exist
     * Deprecated, use _burn(uint256) instead.
     * @param owner owner of the token to burn
     * @param tokenId uint256 ID of the token being burned
     */
    function _burn(address owner, uint256 tokenId) internal {
        require(ownerOf(tokenId) == owner);

        _clearApproval(tokenId);

        _ownedTokensCount[owner] = _ownedTokensCount[owner].sub(1);
        _tokenOwner[tokenId] = address(0);

        emit Transfer(owner, address(0), tokenId);
    }

    /**
     * @dev Internal function to burn a specific token
     * Reverts if the token does not exist
     * @param tokenId uint256 ID of the token being burned
     */
    function _burn(uint256 tokenId) internal {
        _burn(ownerOf(tokenId), tokenId);
    }

    /**
     * @dev Internal function to transfer ownership of a given token ID to another address.
     * As opposed to transferFrom, this imposes no restrictions on msg.sender.
     * @param from current owner of the token
     * @param to address to receive the ownership of the given token ID
     * @param tokenId uint256 ID of the token to be transferred
    */
    function _transferFrom(address from, address to, uint256 tokenId) internal {
        require(ownerOf(tokenId) == from);
        require(to != address(0));

        _clearApproval(tokenId);

        _ownedTokensCount[from] = _ownedTokensCount[from].sub(1);
        _ownedTokensCount[to] = _ownedTokensCount[to].add(1);

        _tokenOwner[tokenId] = to;

        emit Transfer(from, to, tokenId);
    }

    /**
     * @dev Internal function to invoke `onERC721Received` on a target address
     * The call is not executed if the target address is not a contract
     * @param from address representing the previous owner of the given token ID
     * @param to target address that will receive the tokens
     * @param tokenId uint256 ID of the token to be transferred
     * @param _data bytes optional data to send along with the call
     * @return whether the call correctly returned the expected magic value
     */
    function _checkOnERC721Received(address from, address to, uint256 tokenId, bytes memory _data)
        internal returns (bool)
    {
        if (!to.isContract()) {
            return true;
        }

        bytes4 retval = IERC721Receiver(to).onERC721Received(msg.sender, from, tokenId, _data);
        return (retval == _ERC721_RECEIVED);
    }

    /**
     * @dev Private function to clear current approval of a given token ID
     * @param tokenId uint256 ID of the token to be transferred
     */
    function _clearApproval(uint256 tokenId) private {
        if (_tokenApprovals[tokenId] != address(0)) {
            _tokenApprovals[tokenId] = address(0);
        }
    }
}

// File: IERC165.sol



pragma solidity ^0.5.0;

/**
 * @title IERC165
 * @dev https://github.com/ethereum/EIPs/blob/master/EIPS/eip-165.md
 */
interface IERC165 {
    /**
     * @notice Query if a contract implements an interface
     * @param interfaceId The interface identifier, as specified in ERC-165
     * @dev Interface identification is specified in ERC-165. This function
     * uses less than 30,000 gas.
     */
    function supportsInterface(bytes4 interfaceId) external view returns (bool);
}
// File: IERC721.sol



pragma solidity ^0.5.0;

import "./IERC165.sol";

/**
 * @title ERC721 Non-Fungible Token Standard basic interface
 * @dev see https://github.com/ethereum/EIPs/blob/master/EIPS/eip-721.md
 */
contract IERC721 is IERC165 {
    event Transfer(address indexed from, address indexed to, uint256 indexed tokenId);
    event Approval(address indexed owner, address indexed approved, uint256 indexed tokenId);
    event ApprovalForAll(address indexed owner, address indexed operator, bool approved);

    function balanceOf(address owner) public view returns (uint256 balance);
    function ownerOf(uint256 tokenId) public view returns (address owner);

    function approve(address to, uint256 tokenId) public;
    function getApproved(uint256 tokenId) public view returns (address operator);

    function setApprovalForAll(address operator, bool _approved) public;
    function isApprovedForAll(address owner, address operator) public view returns (bool);

    function transferFrom(address from, address to, uint256 tokenId) public;
    function safeTransferFrom(address from, address to, uint256 tokenId) public;

    function safeTransferFrom(address from, address to, uint256 tokenId, bytes memory data) public;
}

// File: IERC721Receiver.sol



pragma solidity ^0.5.0;

/**
 * @title ERC721 token receiver interface
 * @dev Interface for any contract that wants to support safeTransfers
 * from ERC721 asset contracts.
 */
contract IERC721Receiver {
    /**
     * @notice Handle the receipt of an NFT
     * @dev The ERC721 smart contract calls this function on the recipient
     * after a `safeTransfer`. This function MUST return the function selector,
     * otherwise the caller will revert the transaction. The selector to be
     * returned can be obtained as `this.onERC721Received.selector`. This
     * function MAY throw to revert and reject the transfer.
     * Note: the ERC721 contract address is always the message sender.
     * @param operator The address which called `safeTransferFrom` function
     * @param from The address which previously owned the token
     * @param tokenId The NFT identifier which is being transferred
     * @param data Additional data with no specified format
     * @return `bytes4(keccak256("onERC721Received(address,address,uint256,bytes)"))`
     */
    function onERC721Received(address operator, address from, uint256 tokenId, bytes memory data)
    public returns (bytes4);
}

// File: Ownable.sol



pragma solidity ^0.5.0;

/**
 * @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.
     * @notice Renouncing to ownership will leave the contract without an owner.
     * It will not be possible to call the functions with the `onlyOwner`
     * modifier anymore.
     */
    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: SafeMath.sol



pragma solidity ^0.5.0;

/**
 * @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;
    }
}