<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 recursion(int n,int t,vector<vector<int>> &dp){
    //     if(n==0)
    //         return t;
    //     if(dp[n][t]!=-1)
    //         return dp[n][t];
    //     if(t==0){
    //         bool ans=false;
    //         for(int i=1;i<=sqrt(n);++i){
    //             ans|=recursion(n-i*i,1,dp);
    //         }
    //         return dp[n][t]=ans;
    //     }
    //     else{
    //         bool ans=true;
    //         for(int i=1;i<=sqrt(n);++i){
    //             ans&=recursion(n-i*i,0,dp);
    //         }
    //         return dp[n][t]=ans;
    //     }
    // }
    bool winnerSquareGame(int n) {
        vector<vector<int>> dp(n+1,vector<int>(2,0));
        dp[0][0]=0, dp[0][1]=1;
        for(int i=1;i<=n;++i){
            for(int t=0;t<=1;++t){
                if(t==0){
                    bool ans=false;
                    for(int j=1;j<=sqrt(i);++j){
                        ans|=dp[i-j*j][1];
                    }
                    dp[i][t]=ans;
                }
                else{
                    bool ans=true;
                    for(int j=1;j<=sqrt(i);++j){
                        ans&=dp[i-j*j][0];
                    }
                    dp[i][t]=ans;
                }
            }
        }
        return dp[n][0];
    }
};
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