<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:
unordered_map<int , unordered_map<int , int>>check ; 
int solve(int n , int chance){
    if(check[n].count(chance))
    return check[n][chance] ; 
    int temp = 0 ; 
     if(n==0){
        return check[n][chance] = 1 ; 
     }
    if(chance==0){
        int m = sqrt(n) ; 
        while(m>0){
        temp = max(temp , solve(n-m*m , 1) ) ; 
        if(temp)
        return  check[n][chance] = 0 ;
        m-- ;  
        }
    }
    else{
         int m = sqrt(n) ; 
        while(m>0){
        temp = max(temp , solve(n-m*m , 0) ) ; 
        if(temp)
        return  check[n][chance] =  0 ;
        m-- ;  
        }
    }
    return  check[n][chance] = 1 ; 
}
    bool winnerSquareGame(int n) {
       int ans = 0 ; 
       int temp = sqrt(n) ; 
       while(temp>0){
        ans = max(ans , solve(n-temp*temp , 0 )) ; 
        if(ans)
        return true ; 
        temp-- ; 
       }
       return false; 
    }
};
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