613. Find XOR Sum of All Pairs Bitwise AND

0

Hard

The XOR sum of a list is the bitwise XOR of all its elements. If the list only contains one element, then its XOR sum will be equal to this element. For example, the XOR sum of [1,2,3,4] is equal to 1 XOR 2 XOR 3 XOR 4 = 4, and the XOR sum of [3] is equal to 3. You are given two 0-indexed arrays arr1 and arr2 that consist only of non-negative integers. Consider the list containing the result of arr1[i] AND arr2[j] (bitwise AND) for every (i, j) pair where 0 <= i < arr1.length and 0 <= j < arr2.length. Print the XOR sum of the aforementioned list.

Input Format

First line contains size of first array
Second line contains elements of first array
Third line contains size of second array
Fourth line contains elements of second array

Output Format

Integer

Example

Input

3 1 2 3 2 6 5

Output

0

Constraints

1 <= arr1.length, arr2.length <= 105
0 <= arr1[i], arr2[j] <= 109
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