<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:
    m: dict
    def __init__(self) -> None:
        self.m = {}
    def check(self, remains, matchsticks):
        k = (tuple(sorted(remains)), tuple(matchsticks))
        if k in self.m:
            return self.m[k]
        if sum(remains) == 0:
            if len(matchsticks) == 0:
                return True
            else:
                return False
            
        l = matchsticks[0]
        for i in range(4):
            remains[i] -= l
            if remains[i] < 0:
                pass
            else:
                if self.check(remains, matchsticks[1:]):
                    return True
            remains[i] += l
        self.m[k] = False
        return False
            
    def makesquare(self, matchsticks: List[int]) -> bool:
        total = sum(matchsticks)
        if total %4 != 0:
            return False
        length = total // 4
        matchsticks.sort()
        matchsticks.reverse()
        if matchsticks[-1] > length:
            return False
        return self.check([length, length, length, length], matchsticks)
        

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