<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 {
private:
bool isPerfectSqr(int i) {
    int l = 1, r = i, m;
    while(l < r) {
        m = l + (r - l) / 2;
        if (m * 1L * m >= i) r = m;
        else l = m + 1;
    }

    return l * 1L * l == i;
}

int getAns(int n) 
{ 
    int* dp = new int[n + 1]; 
    dp[0] = 0; 
    dp[1] = 1; 
    dp[2] = 0; 
    dp[3] = 1; 
    for (int i = 4; i <= n; i++) { 
        dp[i] = isPerfectSqr(i); 
        for (int x = 1; x <= ceil(sqrt(i)) and !dp[i]; x++) { 
            if(x * x <= i and !dp[i - x * x])  dp[i] = 1;
        } 
    } 
  
    int res = dp[n]; 
    delete[] dp; 
    return res; 
}  

public:
    bool winnerSquareGame(int n) {
        if(n<=3) return n%2;
        return getAns(n);
    }
};
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