<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>

t = 10 ** 9 + 7
x = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192]

class Solution:
    def rec(self, nums1, nums2):

        m = sum(nums1)
        s = sum(nums2)

        if self.dp.get((m, s)) is not None:
            return self.dp[(m, s)]

        nums11 = nums1[1:]
        mini = t
        a = self.dict1[nums1[0]]
        for i in range(len(nums1)):
            b = self.dict2[nums2[i]]
            k = (a ^ b)
            n = self.rec(nums11, nums2[0:i] + nums2[i+1:])
            mini = min(mini, k + n)

        self.dp[(m, s)] = mini
        return mini



    def minimumXORSum(self, nums1: List[int], nums2: List[int]) -> int:
        self.dict1 = {}
        self.dict2 = {}
        self.dp = {(0, 0) : 0}
        for i in range(len(nums1)):
            self.dict1[x[i]] = nums1[i]
            self.dict2[x[i]] = nums2[i]
            nums1[i] = x[i]
            nums2[i] = x[i]
        return self.rec(nums1,  nums2)             
        


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