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

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

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

        return dp[turn][n];
    }
    bool winnerSquareGame(int n) {
        vector<vector<int>> dp (2, vector<int> (n + 1, -1));
        return solve(1, n, dp);
    }
};
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