<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 getarrays(self, sums, ms, msi, target, dp):
        if tuple(sums) in dp:
            return dp[tuple(sums)]
        if msi == len(ms):
            s1, s2, s3, s4 = sums
            return s1 == s2 == s3 == s4
        ans = False
        for i in range(4):
            mli = ms[msi]
            if sums[i] + mli <= target:
                sums[i] += mli
                if self.getarrays(sums, ms, msi + 1, target, dp):
                    ans = True
                    break
                sums[i] -= mli
        dp[tuple(sums)] = ans
        return ans
    
    def makesquare(self, matchsticks: List[int]) -> bool:
        side = sum(matchsticks) // 4
        if side * 4 != sum(matchsticks):
            return False
        sums = [0] * 4
        dp = {}
        matchsticks.sort(reverse=True)
        return self.getarrays(sums, matchsticks, 0, side, dp)
65562