<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:
        N = len(matchsticks)
        sm = sum(matchsticks)
        if sm % 4 != 0:
            return False
        side_len = sm // 4

        matchsticks = sorted(matchsticks, reverse=True)
        memo = {}

        def util(sides_arr=[0,0,0,0], idx=0) -> bool:
            if idx == N:
                return all(side == side_len for side in sides_arr)

            if idx > N: return False

            key = ''.join([f"{i}##" for i in sides_arr])
            if key in memo:
                return memo[key]

            for i in range(4):
                if (sides_arr[i] + matchsticks[idx]) <= side_len:
                    sides_arr[i] += matchsticks[idx]
                    if util(sides_arr, idx+1):
                        memo[key] = True
                        return True
                    sides_arr[i] -= matchsticks[idx]

            memo[key] = False
            return False

        return util()
63767