<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, m: List[int]) -> bool:
        @lru_cache(None)
        def sol(i,l):
            # print(l)
            if i==n:
                if len(set(l))==1:
                    return True
                return False
            
            a=False
            if m[i]+l[0]<=summ:
                tmp1=list(l[:])
                tmp1[0]+=m[i]
                a=a or sol(i+1,tuple(tmp1))
                if a:
                    return True
            if m[i]+l[1]<=summ:
                tmp2=list(l[:])
                tmp2[1]+=m[i]
                a=a or sol(i+1,tuple(tmp2))
                if a:
                    return True
            if m[i]+l[2]<=summ:
                tmp3=list(l[:])
                tmp3[2]+=m[i]
                a=a or sol(i+1,tuple(tmp3))
                if a:
                    return True
            if m[i]+l[3]<=summ:
                tmp4=list(l[:])
                tmp4[3]+=m[i]
                a=a or sol(i+1,tuple(tmp4))
                return a
            return False
        if sum(m)%4!=0:
            return False
        summ=sum(m)//4
        n=len(m)
        m.sort(reverse=True)
        return sol(0,(0,0,0,0))
79922