826. Minimum XOR Sum of Two Arrays (Bitmask Recursion)

Given two integer arrays a and b of equal length n, rearrange b to minimize the sum of a[i] XOR b[perm[i]] for all i. Return the minimum XOR sum. Input: JSON {a, b}.

Input: JSON {a, b}.

Output: Integer.

Examples

Input: {"a":[1,2],"b":[2,3]}
Output: 2
Explanation: 1^3 + 2^2 = 2+0 = 2.

Input: {"a":[1,0,3],"b":[5,3,4]}
Output: 8
Explanation: Optimal assignment yields XOR sum 8.

Constraints

• 1 <= n <= 14
• 0 <= a[i], b[i] <= 10^7

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