<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 {
public:
    bool solve(int n,int turn,vector<vector<int>>&dp){
         
         if(turn == 1  && n==0)return true;
         if(turn == 0 && n==0)return false;

         if(dp[n][turn]!=-1)return dp[n][turn];

         bool ans=(turn == 0)?false:true;

         for(int i=1;i*i<=n;i++){
             
             if(turn == 0 ){
                 ans = ans || solve(n-i*i,1,dp);
             }
             else{
                ans= ans && solve(n-i*i,0,dp);
             }
         }

         return dp[n][turn]=ans;
    }
    bool winnerSquareGame(int n) {

        vector<vector<int>>dp(n+1,vector<int>(3,-1));

        return solve(n,0,dp);
        
    }
};
28334