pragma solidity ^0.4.20;
 
/*
* ====================================*
*
* PROOF OF RIPPLE
* https://poripple.com/
* https://discord.gg/6AA5etr
*
* ====================================*
*
* -> How is Proof of Ripple different than other Proof Coin?
* Proof of Ripple is a more sustainable contract with the innovative 4X Wagering Requirement mechanics.
* The total amount of all sold tokens and reinvested tokens must be at least 4 times the total purchased tokens before you can withdraw.
*
* -> Here is an example illustrating how it works:
* Let say initially you purchased 500 PoRipple tokens, and sold all 500 tokens later, at that point, you cannot immediately withdraw because the 4X Wagering Requirement haven't met yet, you'll need to reinvest your balance in order to increase the total wagering amount.
* Now suppose the tokens price dropped a bit later on, and you're able to reinvest the dividends and get 750 tokens, so if you sell all 750 tokens, you'll be able to withdraw all your balance, because the 4X Wagering Requirement is fulfilled, i.e. Total Wagered Tokens (500 sell + 750 reinvest + 750 sell) = 4 x Total Purchased Tokens (500 initial purchase)
*
* -> What is the advantages of wagering:
* 1. Unlike all other PO clones, early buyers cannot just dump and exit in PoRipple, because they'll need to reinvest it back in order to fulfill the 4X Wagering Requirement.
* 2. It incentivize token holding, and gathering dividends instead of fomo dumping.
* 3. It induce higher volatility, more actions = more dividends for holders!
* 4. People will feel more comfortable buying in later stage.
*
* -> What?
* The original autonomous pyramid, improved:
* [x] More stable than ever, having withstood severe testnet abuse and attack attempts from our community!.
* [x] Audited, tested, and approved by known community security specialists such as tocsick and Arc.
* [X] New functionality; you can now perform partial sell orders. If you succumb to weak hands, you don't have to dump all of your bags!
* [x] New functionality; you can now transfer tokens between wallets. Trading is now possible from within the contract!
* [x] New Feature: PoS Masternodes! The first implementation of Ethereum Staking in the world! Vitalik is mad.
* [x] Masternodes: Holding 50 PoRipple Tokens allow you to generate a Masternode link, Masternode links are used as unique entry points to the contract!
* [x] Masternodes: All players who enter the contract through your Masternode have 30% of their 20% dividends fee rerouted from the master-node, to the node-master!
*
* -> What about the last projects?
* Every programming member of the old dev team has been fired and/or killed by 232.
* The new dev team consists of seasoned, professional developers and has been audited by veteran solidity experts.
* Additionally, two independent testnet iterations have been used by hundreds of people; not a single point of failure was found.
*
* -> Who worked on this project?
* Trusted community from CryptoGaming
*
*/
 
contract ProofOfRipple {
    /*=================================
    =            MODIFIERS            =
    =================================*/
    // only people with tokens
    modifier onlyBagholders() {
        require(myTokens() > 0);
        _;
    }
 
    // only people with profits
    modifier onlyStronghands() {
        require(myDividends(true) > 0);
        _;
    }
 
    modifier onlyWageredWithdraw() {
       address _customerAddress = msg.sender;
       require(wageringOf_[_customerAddress] >= SafeMath.mul(initialBuyinOf_[_customerAddress], wageringRequirement_));
       _;
    }
 
    // administrators can:
    // -> change the name of the contract
    // -> change the name of the token
    // -> change the PoS difficulty (How many tokens it costs to hold a masternode, in case it gets crazy high later)
    // they CANNOT:
    // -> take funds
    // -> disable withdrawals
    // -> kill the contract
    // -> change the price of tokens
    modifier onlyAdministrator(){
        address _customerAddress = msg.sender;
        require(administrators[_customerAddress]);
        _;
    }
 
 
    // ensures that the first tokens in the contract will be equally distributed
    // meaning, no divine dump will be ever possible
    // result: healthy longevity.
    modifier antiEarlyWhale(uint256 _amountOfEthereum){
        address _customerAddress = msg.sender;
 
        // are we still in the vulnerable phase?
        // if so, enact anti early whale protocol
        if( onlyAmbassadors && ((totalEthereumBalance() - _amountOfEthereum) <= ambassadorQuota_ )){
            require(
                // is the customer in the ambassador list?
                ambassadors_[_customerAddress] == true &&
 
                // does the customer purchase exceed the max ambassador quota?
                (ambassadorAccumulatedQuota_[_customerAddress] + _amountOfEthereum) <= ambassadorMaxPurchase_
 
            );
 
            // updated the accumulated quota
            ambassadorAccumulatedQuota_[_customerAddress] = SafeMath.add(ambassadorAccumulatedQuota_[_customerAddress], _amountOfEthereum);
 
            // execute
            _;
        } else {
            // in case the ether count drops low, the ambassador phase won't reinitiate
            onlyAmbassadors = false;
            _;
        }
 
    }
 
 
    /*==============================
    =            EVENTS            =
    ==============================*/
    event onTokenPurchase(
        address indexed customerAddress,
        uint256 incomingEthereum,
        uint256 tokensMinted,
        address indexed referredBy,
        uint256 timestamp,
        uint256 price
    );
 
    event onTokenSell(
        address indexed customerAddress,
        uint256 tokensBurned,
        uint256 ethereumEarned,
        uint256 timestamp,
        uint256 price
    );
 
    event onReinvestment(
        address indexed customerAddress,
        uint256 ethereumReinvested,
        uint256 tokensMinted
    );
 
    event onWithdraw(
        address indexed customerAddress,
        uint256 ethereumWithdrawn
    );
 
    // ERC20
    event Transfer(
        address indexed from,
        address indexed to,
        uint256 tokens
    );
 
 
    /*=====================================
    =            CONFIGURABLES            =
    =====================================*/
    string public name = "ProofOfRipple";
    string public symbol = "PoRipple";
    uint8 constant public decimals = 18;
    uint8 constant internal dividendFee_ = 5; // 20% dividends on buy and sell and transfer
    uint256 constant internal tokenPriceInitial_ = 0.0000001 ether;
    uint256 constant internal tokenPriceIncremental_ = 0.00000001 ether;
    uint256 constant internal magnitude = 2**64;
    uint256 constant internal wageringRequirement_ = 4; // 4x is wagering requirement for the pyramid
 
    // proof of stake (defaults at 100 tokens)
    uint256 public stakingRequirement = 50e18;
 
    // ambassador program
    mapping(address => bool) internal ambassadors_;
    uint256 constant internal ambassadorMaxPurchase_ = 0.4 ether; // only 0.4 eth premine
    uint256 constant internal ambassadorQuota_ = 2 ether;
 
 
 
   /*================================
    =            DATASETS            =
    ================================*/
    mapping(address => uint256) public initialBuyinOf_; // amount of tokens bought in pyramid
    mapping(address => uint256) public wageringOf_; // wagering amount of tokens for the user
 
    // amount of shares for each address (scaled number)
    mapping(address => uint256) internal tokenBalanceLedger_;
    mapping(address => uint256) internal referralBalance_;
    mapping(address => int256) internal payoutsTo_;
    mapping(address => uint256) internal ambassadorAccumulatedQuota_;
    uint256 internal tokenSupply_ = 0;
    uint256 internal profitPerShare_;
 
    // administrator list (see above on what they can do)
    mapping(address => bool) public administrators;
 
    // when this is set to true, only ambassadors can purchase tokens (this prevents a whale premine, it ensures a fairly distributed upper pyramid)
    bool public onlyAmbassadors = true;
 
 
 
    /*=======================================
    =            PUBLIC FUNCTIONS            =
    =======================================*/
    /*
    * -- APPLICATION ENTRY POINTS --
    */
    function ProofOfRipple()
        public
    {
        // add administrators here
        administrators[0x15Fda64fCdbcA27a60Aa8c6ca882Aa3e1DE4Ea41] = true;
        ambassadors_[0x15Fda64fCdbcA27a60Aa8c6ca882Aa3e1DE4Ea41] = true;
        ambassadors_[0xFEA0904ACc8Df0F3288b6583f60B86c36Ea52AcD] = true;
        ambassadors_[0x494952f01a30547d269aaF147e6226f940f5B041] = true;
    }
 
 
    /**
     * Converts all incoming ethereum to tokens for the caller, and passes down the referral addy (if any)
     */
    function buy(address _referredBy)
        public
        payable
        returns(uint256)
    {
        purchaseTokens(msg.value, _referredBy, false);
    }
 
    /**
     * Fallback function to handle ethereum that was send straight to the contract
     * Unfortunately we cannot use a referral address this way.
     */
    function()
        payable
        public
    {
        purchaseTokens(msg.value, 0x0, false);
    }
 
    /**
     * Converts all of caller's dividends to tokens.
     */
    function reinvest()
        onlyStronghands()
        public
    {
        // fetch dividends
        uint256 _dividends = myDividends(false); // retrieve ref. bonus later in the code
 
        // pay out the dividends virtually
        address _customerAddress = msg.sender;
        payoutsTo_[_customerAddress] +=  (int256) (_dividends * magnitude);
 
        // retrieve ref. bonus
        _dividends += referralBalance_[_customerAddress];
        referralBalance_[_customerAddress] = 0;
 
        // dispatch a buy order with the virtualized "withdrawn dividends"
        uint256 _tokens = purchaseTokens(_dividends, 0x0, true);
 
        // fire event
        onReinvestment(_customerAddress, _dividends, _tokens);
    }
 
    /**
     * Alias of sell() and withdraw().
     */
    function exit()
        public
    {
        // get token count for caller & sell them all
        address _customerAddress = msg.sender;
        uint256 _tokens = tokenBalanceLedger_[_customerAddress];
        if(_tokens > 0) sell(_tokens);
 
        // lambo delivery service
        withdraw();
    }
 
    /**
     * Withdraws all of the callers earnings.
     */
    function withdraw()
        onlyStronghands()
        onlyWageredWithdraw()
        public
    {
        // setup data
        address _customerAddress = msg.sender;
        uint256 _dividends = myDividends(false); // get ref. bonus later in the code
 
        // update dividend tracker
        payoutsTo_[_customerAddress] +=  (int256) (_dividends * magnitude);
 
        // add ref. bonus
        _dividends += referralBalance_[_customerAddress];
        referralBalance_[_customerAddress] = 0;
 
        // lambo delivery service
        _customerAddress.transfer(_dividends);
 
        // fire event
        onWithdraw(_customerAddress, _dividends);
    }
 
    /**
     * Liquifies tokens to ethereum.
     */
    function sell(uint256 _amountOfTokens)
        onlyBagholders()
        public
    {
        // setup data
        address _customerAddress = msg.sender;
        // russian hackers BTFO
        require(_amountOfTokens <= tokenBalanceLedger_[_customerAddress]);
        uint256 _tokens = _amountOfTokens;
        uint256 _ethereum = tokensToEthereum_(_tokens);
        uint256 _dividends = SafeMath.div(_ethereum, dividendFee_);
        uint256 _taxedEthereum = SafeMath.sub(_ethereum, _dividends);
 
        // burn the sold tokens
        tokenSupply_ = SafeMath.sub(tokenSupply_, _tokens);
        tokenBalanceLedger_[_customerAddress] = SafeMath.sub(tokenBalanceLedger_[_customerAddress], _tokens);
        // Update wagering balance of the user, add the sold amount of tokens
        wageringOf_[_customerAddress] = SafeMath.add(wageringOf_[_customerAddress], _tokens);
 
        // update dividends tracker
        int256 _updatedPayouts = (int256) (profitPerShare_ * _tokens + (_taxedEthereum * magnitude));
        payoutsTo_[_customerAddress] -= _updatedPayouts;
 
        // dividing by zero is a bad idea
        if (tokenSupply_ > 0) {
            // update the amount of dividends per token
            profitPerShare_ = SafeMath.add(profitPerShare_, (_dividends * magnitude) / tokenSupply_);
        }
 
        // fire event
        onTokenSell(_customerAddress, _tokens, _taxedEthereum, now, buyPrice());
    }
 
 
    /**
     * Transfer tokens from the caller to a new holder.
     * Remember, there's a 20% fee here as well.
     */
    function transfer(address _toAddress, uint256 _amountOfTokens)
        onlyBagholders()
        public
        returns(bool)
    {
        // setup
        address _customerAddress = msg.sender;
 
        // make sure we have the requested tokens
        // also disables transfers until ambassador phase is over
        // ( we dont want whale premines )
        require(!onlyAmbassadors && _amountOfTokens <= tokenBalanceLedger_[_customerAddress]);
 
        // withdraw all outstanding dividends first
        if(myDividends(true) > 0) withdraw();
 
        // liquify 20% of the tokens that are transfered
        // these are dispersed to shareholders
        uint256 _tokenFee = SafeMath.div(_amountOfTokens, dividendFee_);
        uint256 _taxedTokens = SafeMath.sub(_amountOfTokens, _tokenFee);
        uint256 _dividends = tokensToEthereum_(_tokenFee);
 
        // burn the fee tokens
        tokenSupply_ = SafeMath.sub(tokenSupply_, _tokenFee);
 
        // exchange tokens
        tokenBalanceLedger_[_customerAddress] = SafeMath.sub(tokenBalanceLedger_[_customerAddress], _amountOfTokens);
        tokenBalanceLedger_[_toAddress] = SafeMath.add(tokenBalanceLedger_[_toAddress], _taxedTokens);
 
        // Update wagering balance of the user, add the transfer amount tokens
        wageringOf_[_customerAddress] = SafeMath.add(wageringOf_[_customerAddress], _amountOfTokens);
        // Update wagering balance and buyin fee for the user tokens transfered to
        initialBuyinOf_[_toAddress] = SafeMath.add(initialBuyinOf_[_toAddress], _taxedTokens);
 
        // update dividend trackers
        payoutsTo_[_customerAddress] -= (int256) (profitPerShare_ * _amountOfTokens);
        payoutsTo_[_toAddress] += (int256) (profitPerShare_ * _taxedTokens);
 
        // disperse dividends among holders
        profitPerShare_ = SafeMath.add(profitPerShare_, (_dividends * magnitude) / tokenSupply_);
 
        // fire event
        Transfer(_customerAddress, _toAddress, _taxedTokens);
 
        // ERC20
        return true;
 
    }
 
    /*----------  ADMINISTRATOR ONLY FUNCTIONS  ----------*/
    /**
     * In case the amassador quota is not met, the administrator can manually disable the ambassador phase.
     */
    function disableInitialStage()
        onlyAdministrator()
        public
    {
        onlyAmbassadors = false;
    }
 
    /**
     * In case one of us dies, we need to replace ourselves.
     */
    function setAdministrator(address _identifier, bool _status)
        onlyAdministrator()
        public
    {
        administrators[_identifier] = _status;
    }
 
    /**
     * Precautionary measures in case we need to adjust the masternode rate.
     */
    function setStakingRequirement(uint256 _amountOfTokens)
        onlyAdministrator()
        public
    {
        stakingRequirement = _amountOfTokens;
    }
 
    /**
     * If we want to rebrand, we can.
     */
    function setName(string _name)
        onlyAdministrator()
        public
    {
        name = _name;
    }
 
    /**
     * If we want to rebrand, we can.
     */
    function setSymbol(string _symbol)
        onlyAdministrator()
        public
    {
        symbol = _symbol;
    }
 
 
    /*----------  HELPERS AND CALCULATORS  ----------*/
    /**
     * Method to view the current Ethereum stored in the contract
     * Example: totalEthereumBalance()
     */
    function totalEthereumBalance()
        public
        view
        returns(uint)
    {
        return this.balance;
    }
 
    /**
     * Retrieve the total token supply.
     */
    function totalSupply()
        public
        view
        returns(uint256)
    {
        return tokenSupply_;
    }
 
    /**
     * Retrieve the tokens owned by the caller.
     */
    function myTokens()
        public
        view
        returns(uint256)
    {
        address _customerAddress = msg.sender;
        return balanceOf(_customerAddress);
    }
 
    /**
     * Retrieve the dividends owned by the caller.
     * If `_includeReferralBonus` is to to 1/true, the referral bonus will be included in the calculations.
     * The reason for this, is that in the frontend, we will want to get the total divs (global + ref)
     * But in the internal calculations, we want them separate.
     */
    function myDividends(bool _includeReferralBonus)
        public
        view
        returns(uint256)
    {
        address _customerAddress = msg.sender;
        return _includeReferralBonus ? dividendsOf(_customerAddress) + referralBalance_[_customerAddress] : dividendsOf(_customerAddress) ;
    }
 
    /**
     * Retrieve the token balance of any single address.
     */
    function balanceOf(address _customerAddress)
        view
        public
        returns(uint256)
    {
        return tokenBalanceLedger_[_customerAddress];
    }
 
    /**
     * Retrieve the dividend balance of any single address.
     */
    function dividendsOf(address _customerAddress)
        view
        public
        returns(uint256)
    {
        return (uint256) ((int256)(profitPerShare_ * tokenBalanceLedger_[_customerAddress]) - payoutsTo_[_customerAddress]) / magnitude;
    }
 
    /**
     * Return the buy price of 1 individual token.
     */
    function sellPrice()
        public
        view
        returns(uint256)
    {
        // our calculation relies on the token supply, so we need supply. Doh.
        if(tokenSupply_ == 0){
            return tokenPriceInitial_ - tokenPriceIncremental_;
        } else {
            uint256 _ethereum = tokensToEthereum_(1e18);
            uint256 _dividends = SafeMath.div(_ethereum, dividendFee_  );
            uint256 _taxedEthereum = SafeMath.sub(_ethereum, _dividends);
            return _taxedEthereum;
        }
    }
 
    /**
     * Return the sell price of 1 individual token.
     */
    function buyPrice()
        public
        view
        returns(uint256)
    {
        // our calculation relies on the token supply, so we need supply. Doh.
        if(tokenSupply_ == 0){
            return tokenPriceInitial_ + tokenPriceIncremental_;
        } else {
            uint256 _ethereum = tokensToEthereum_(1e18);
            uint256 _dividends = SafeMath.div(_ethereum, dividendFee_  );
            uint256 _taxedEthereum = SafeMath.add(_ethereum, _dividends);
            return _taxedEthereum;
        }
    }
 
    /**
     * Function for the frontend to dynamically retrieve the price scaling of buy orders.
     */
    function calculateTokensReceived(uint256 _ethereumToSpend)
        public
        view
        returns(uint256)
    {
        uint256 _dividends = SafeMath.div(_ethereumToSpend, dividendFee_);
        uint256 _taxedEthereum = SafeMath.sub(_ethereumToSpend, _dividends);
        uint256 _amountOfTokens = ethereumToTokens_(_taxedEthereum);
 
        return _amountOfTokens;
    }
 
    /**
     * Function for the frontend to dynamically retrieve the price scaling of sell orders.
     */
    function calculateEthereumReceived(uint256 _tokensToSell)
        public
        view
        returns(uint256)
    {
        require(_tokensToSell <= tokenSupply_);
        uint256 _ethereum = tokensToEthereum_(_tokensToSell);
        uint256 _dividends = SafeMath.div(_ethereum, dividendFee_);
        uint256 _taxedEthereum = SafeMath.sub(_ethereum, _dividends);
        return _taxedEthereum;
    }
 
 
    /*==========================================
    =            INTERNAL FUNCTIONS            =
    ==========================================*/
    function purchaseTokens(uint256 _incomingEthereum, address _referredBy,  bool _isReinvest)
        antiEarlyWhale(_incomingEthereum)
        internal
        returns(uint256)
    {
        // data setup
        uint256 _undividedDividends = SafeMath.div(_incomingEthereum, dividendFee_);
        uint256 _referralBonus = SafeMath.div(_undividedDividends, 3);
        uint256 _dividends = SafeMath.sub(_undividedDividends, _referralBonus);
        uint256 _taxedEthereum = SafeMath.sub(_incomingEthereum, _undividedDividends);
        uint256 _amountOfTokens = ethereumToTokens_(_taxedEthereum);
        uint256 _fee = _dividends * magnitude;
 
        // no point in continuing execution if OP is a poorfag russian hacker
        // prevents overflow in the case that the pyramid somehow magically starts being used by everyone in the world
        // (or hackers)
        // and yes we know that the safemath function automatically rules out the "greater then" equasion.
        require(_amountOfTokens > 0 && (SafeMath.add(_amountOfTokens,tokenSupply_) > tokenSupply_));
 
        // is the user referred by a masternode?
        if(
            // is this a referred purchase?
            _referredBy != 0x0000000000000000000000000000000000000000 &&
 
            // no cheating!
            _referredBy != msg.sender &&
 
            // does the referrer have at least X whole tokens?
            // i.e is the referrer a godly chad masternode
            tokenBalanceLedger_[_referredBy] >= stakingRequirement
        ){
            // wealth redistribution
            referralBalance_[_referredBy] = SafeMath.add(referralBalance_[_referredBy], _referralBonus);
        } else {
            // no ref purchase
            // add the referral bonus back to the global dividends cake
            _dividends = SafeMath.add(_dividends, _referralBonus);
            _fee = _dividends * magnitude;
        }
 
        // we can't give people infinite ethereum
        if(tokenSupply_ > 0){
 
            // add tokens to the pool
            tokenSupply_ = SafeMath.add(tokenSupply_, _amountOfTokens);
 
            // take the amount of dividends gained through this transaction, and allocates them evenly to each shareholder
            profitPerShare_ += (_dividends * magnitude / (tokenSupply_));
 
            // calculate the amount of tokens the customer receives over his purchase
            _fee = _fee - (_fee-(_amountOfTokens * (_dividends * magnitude / (tokenSupply_))));
 
        } else {
            // add tokens to the pool
            tokenSupply_ = _amountOfTokens;
        }
 
        // update circulating supply & the ledger address for the customer
        tokenBalanceLedger_[msg.sender] = SafeMath.add(tokenBalanceLedger_[msg.sender], _amountOfTokens);
 
        
        if (_isReinvest) {
            // Update the Wagering Balance for the customer
            wageringOf_[msg.sender] = SafeMath.add(wageringOf_[msg.sender], _amountOfTokens);
        } else {
          // If it is not reinvest update initial Buy In amount
          initialBuyinOf_[msg.sender] = SafeMath.add(initialBuyinOf_[msg.sender], _amountOfTokens);
        }
 
        // Tells the contract that the buyer doesn't deserve dividends for the tokens before they owned them;
        //really i know you think you do but you don't
        int256 _updatedPayouts = (int256) ((profitPerShare_ * _amountOfTokens) - _fee);
        payoutsTo_[msg.sender] += _updatedPayouts;
 
        // fire event
        onTokenPurchase(msg.sender, _incomingEthereum, _amountOfTokens, _referredBy, now, buyPrice());
 
        return _amountOfTokens;
    }
 
    /**
     * Calculate Token price based on an amount of incoming ethereum
     * It's an algorithm, hopefully we gave you the whitepaper with it in scientific notation;
     * Some conversions occurred to prevent decimal errors or underflows / overflows in solidity code.
     */
    function ethereumToTokens_(uint256 _ethereum)
        internal
        view
        returns(uint256)
    {
        uint256 _tokenPriceInitial = tokenPriceInitial_ * 1e18;
        uint256 _tokensReceived =
         (
            (
                // underflow attempts BTFO
                SafeMath.sub(
                    (sqrt
                        (
                            (_tokenPriceInitial**2)
                            +
                            (2*(tokenPriceIncremental_ * 1e18)*(_ethereum * 1e18))
                            +
                            (((tokenPriceIncremental_)**2)*(tokenSupply_**2))
                            +
                            (2*(tokenPriceIncremental_)*_tokenPriceInitial*tokenSupply_)
                        )
                    ), _tokenPriceInitial
                )
            )/(tokenPriceIncremental_)
        )-(tokenSupply_)
        ;
 
        return _tokensReceived;
    }
 
    /**
     * Calculate token sell value.
     * It's an algorithm, hopefully we gave you the whitepaper with it in scientific notation;
     * Some conversions occurred to prevent decimal errors or underflows / overflows in solidity code.
     */
     function tokensToEthereum_(uint256 _tokens)
        internal
        view
        returns(uint256)
    {
 
        uint256 tokens_ = (_tokens + 1e18);
        uint256 _tokenSupply = (tokenSupply_ + 1e18);
        uint256 _etherReceived =
        (
            // underflow attempts BTFO
            SafeMath.sub(
                (
                    (
                        (
                            tokenPriceInitial_ +(tokenPriceIncremental_ * (_tokenSupply/1e18))
                        )-tokenPriceIncremental_
                    )*(tokens_ - 1e18)
                ),(tokenPriceIncremental_*((tokens_**2-tokens_)/1e18))/2
            )
        /1e18);
        return _etherReceived;
    }
 
 
    //This is where all your gas goes, sorry
    //Not sorry, you probably only paid 1 gwei
    function sqrt(uint x) internal pure returns (uint y) {
        uint z = (x + 1) / 2;
        y = x;
        while (z < y) {
            y = z;
            z = (x / z + z) / 2;
        }
    }
}
 
/**
 * @title SafeMath
 * @dev Math operations with safety checks that throw on error
 */
library SafeMath {
 
    /**
    * @dev Multiplies two numbers, throws on overflow.
    */
    function mul(uint256 a, uint256 b) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }
        uint256 c = a * b;
        assert(c / a == b);
        return c;
    }
 
    /**
    * @dev Integer division of two numbers, truncating the quotient.
    */
    function div(uint256 a, uint256 b) internal pure 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;
    }
 
    /**
    * @dev Substracts two numbers, throws on overflow (i.e. if subtrahend is greater than minuend).
    */
    function sub(uint256 a, uint256 b) internal pure returns (uint256) {
        assert(b <= a);
        return a - b;
    }
 
    /**
    * @dev Adds two numbers, throws on overflow.
    */
    function add(uint256 a, uint256 b) internal pure returns (uint256) {
        uint256 c = a + b;
        assert(c >= a);
        return c;
    }
}