<p>You are given two integer arrays <code>nums1</code> and <code>nums2</code> of length <code>n</code>.</p>

<p>The <strong>XOR sum</strong> of the two integer arrays is <code>(nums1[0] XOR nums2[0]) + (nums1[1] XOR nums2[1]) + ... + (nums1[n - 1] XOR nums2[n - 1])</code> (<strong>0-indexed</strong>).</p>

<ul>
	<li>For example, the <strong>XOR sum</strong> of <code>[1,2,3]</code> and <code>[3,2,1]</code> is equal to <code>(1 XOR 3) + (2 XOR 2) + (3 XOR 1) = 2 + 0 + 2 = 4</code>.</li>
</ul>

<p>Rearrange the elements of <code>nums2</code> such that the resulting <strong>XOR sum</strong> is <b>minimized</b>.</p>

<p>Return <em>the <strong>XOR sum</strong> after the rearrangement</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums1 = [1,2], nums2 = [2,3]
<strong>Output:</strong> 2
<b>Explanation:</b> Rearrange <code>nums2</code> so that it becomes <code>[3,2]</code>.
The XOR sum is (1 XOR 3) + (2 XOR 2) = 2 + 0 = 2.</pre>

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

<pre>
<strong>Input:</strong> nums1 = [1,0,3], nums2 = [5,3,4]
<strong>Output:</strong> 8
<b>Explanation:</b> Rearrange <code>nums2</code> so that it becomes <code>[5,4,3]</code>. 
The XOR sum is (1 XOR 5) + (0 XOR 4) + (3 XOR 3) = 4 + 4 + 0 = 8.
</pre>

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

<ul>
	<li><code>n == nums1.length</code></li>
	<li><code>n == nums2.length</code></li>
	<li><code>1 &lt;= n &lt;= 14</code></li>
	<li><code>0 &lt;= nums1[i], nums2[i] &lt;= 10<sup>7</sup></code></li>
</ul>

class Solution:
    def minimumXORSum(self, nums1: List[int], nums2: List[int]) -> int:
        n=len(nums1)
        dp=[[float("inf")]*(1<<n) for _ in range(n)]
        

        for i in range(n-1,-1,-1):
            for mask in range((1<<n)-1,-1,-1):
                temp=float("inf")
                for j in range(n):
                    if  mask&(1<<j):
                        continue
                    res=dp[i+1][mask|(1<<j)] if (i+1)<n else 0
                    temp=min(temp,(nums1[i]^nums2[j])+res) 
                dp[i][mask]=temp
               
        return dp[0][0]
       
25300