<p>Alice and Bob take turns playing a game, with Alice starting first.</p>

<p>Initially, there are <code>n</code> stones in a pile. On each player&#39;s turn, that player makes a <em>move</em> consisting of removing <strong>any</strong> non-zero <strong>square number</strong> of stones in the pile.</p>

<p>Also, if a player cannot make a move, he/she loses the game.</p>

<p>Given a positive integer <code>n</code>, return <code>true</code> if and only if Alice wins the game otherwise return <code>false</code>, assuming both players play optimally.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> true
<strong>Explanation: </strong>Alice can remove 1 stone winning the game because Bob doesn&#39;t have any moves.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> false
<strong>Explanation: </strong>Alice can only remove 1 stone, after that Bob removes the last one winning the game (2 -&gt; 1 -&gt; 0).
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> true
<strong>Explanation:</strong> n is already a perfect square, Alice can win with one move, removing 4 stones (4 -&gt; 0).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
    vector<vector<int>> dp;
    bool solve(int n,bool turn)
    {
        if(n==0)
        return !turn;
        if(dp[n][turn]!=-1)
        return dp[n][turn];
        for(int i=sqrt(n);i>=1;i--)
        {

            if(solve(n-i*i,!turn)==turn)
            return dp[n][turn]=turn;
        }
        return dp[n][turn]=!turn;
    }
    // bool solve(int n)
    // {
    //     vector<vector<int>> dp(n+1,vector<int>(2,0));
    //     dp[0][0]=true;
    //     dp[0][1]=false;
    //     for(int i=1;i<=n;i++)
    //     {
    //         // turn -> 0 alice
    //         for(int j=sqrt(i);j>=1;j--)
    //         {
    //             if(dp[i-j*j][1]==0)
    //             dp[i][0]=0;
    //         }
    //         dp[i][0]
    //     }
    // }
public:
    bool winnerSquareGame(int n) {
        dp.resize(n+1,vector<int>(2,-1));
        return solve(n,true);
    }
};
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