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Problem · Array

Product of XOR of All Good Pairs

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Problem statement

Given an array of size N, find the product of XOR of all good pairs in the array. A pair (A[i],A[j]) is called good only when 0 <= i < j < N. Since the product of good pairs might be too large, hence print product % 1e9+7.

Input Format

The first line of input contains T - number of test cases. The first line of each test case contains N - the size of the array. The second line of each test case contains the N elements.

Output Format

Print the product of XOR of all good pairs in the array.

Constraints

30 points 2 <= N <= 10^3

70 points 2 <= N <= 10^5

General Constraints 1 <= T <= 10 1 <= A[i] <= 3000

Function

productOfXOROfAllGoodPairs(A: int[]) → int

Examples

Example 1

A = [1, 2, 3, 7]return = 720

Example 1: (1^2) * (1^3) * (1^7) * (2^3) * (2^7) * (3^7) = 720

Example 2

A = [4, 3, 7]return = 84

Example 2: (4^3) * (4^7) * (3^7) = 84

Constraints

See above