<p>You are given an integer array <code>matchsticks</code> where <code>matchsticks[i]</code> is the length of the <code>i<sup>th</sup></code> matchstick. You want to use <strong>all the matchsticks</strong> to make one square. You <strong>should not break</strong> any stick, but you can link them up, and each matchstick must be used <strong>exactly one time</strong>.</p>

<p>Return <code>true</code> if you can make this square and <code>false</code> otherwise.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/09/matchsticks1-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
<strong>Input:</strong> matchsticks = [1,1,2,2,2]
<strong>Output:</strong> true
<strong>Explanation:</strong> You can form a square with length 2, one side of the square came two sticks with length 1.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> matchsticks = [3,3,3,3,4]
<strong>Output:</strong> false
<strong>Explanation:</strong> You cannot find a way to form a square with all the matchsticks.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= matchsticks.length &lt;= 15</code></li>
	<li><code>1 &lt;= matchsticks[i] &lt;= 10<sup>8</sup></code></li>
</ul>

class Solution:
    def makesquare(self, matchsticks: List[int]) -> bool:
        if len(matchsticks)<4 or sum(matchsticks)%4:
            return False
        
        side = sum(matchsticks) // 4

        if max(matchsticks)> side:
            return False
        
        matchsticks.sort(reverse= True)
        
        mem = {}
        
        def recur(a, b, c, d, i):
            if a> side or b>side or c>side or d>side:
                return False
            if i== len(matchsticks):
                return True
        
            if (a, b, c, d, i) in mem:
                return mem[(a, b, c, d, i)]
            
            val = matchsticks[i]
            x1= recur(a+val, b, c, d, i+1) or  recur(a, b+val, c, d, i+1)
            if x1:
                mem[(a, b, c, d, i)] = True
                return True
            x2= recur(a, b, c+val, d, i+1) or recur(a, b, c, d+val, i+1)
            mem[(a, b, c, d, i)] = x2
            return x2
        
        return recur(matchsticks[0], 0, 0, 0, 1)

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