Luntik came out for a morning stroll and found an array a of length n. He calculated the sum s of the elements of the array (s= ∑_{i=1}^{n} a_i). Luntik calls a subsequence of the array a nearly full if the sum of the numbers in that subsequence is equal to s-1.

Luntik really wants to know the number of nearly full subsequences of the array a. But he needs to come home so he asks you to solve that problem!

A sequence x is a subsequence of a sequence y if x can be obtained from y by deletion of several (possibly, zero or all) elements.

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases. The next 2 ⋅ t lines contain descriptions of test cases. The description of each test case consists of two lines.

The first line of each test case contains a single integer n (1 ≤ n ≤ 60) — the length of the array.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — the elements of the array a.

Output

For each test case print the number of nearly full subsequences of the array.

Example

Input


5
5
1 2 3 4 5
2
1000 1000
2
1 0
5
3 0 2 1 1
5
2 1 0 3 0


Output


1
0
2
4
4

Note

In the first test case, s=1+2+3+4+5=15, only (2,3,4,5) is a nearly full subsequence among all subsequences, the sum in it is equal to 2+3+4+5=14=15-1.

In the second test case, there are no nearly full subsequences.

In the third test case, s=1+0=1, the nearly full subsequences are (0) and () (the sum of an empty subsequence is 0).
import random
from datetime import datetime


def read_nums():
    return [int(x) for x in input().split()]


def unique(nums):
    seen = set()
    res = []
    for num in nums:
        if num not in seen:
            res.append(num)
            seen.add(num)

    return res


def solve(nums):
    nums = unique(nums)

    seqs = {0: 0}  # (x -> max_value )
    for num in nums:
        for x in sorted(seqs):
            max_val = seqs[x]
            if num > max_val:
                new_x = x ^ num
                if new_x not in seqs:
                    seqs[new_x] = num
                elif num < seqs[new_x]:
                    seqs[new_x] = num
            else:
                break

    print(len(seqs))
    print(' '.join(map(str, sorted(seqs))))


def main():
    n, = read_nums()
    nums = read_nums()
    # nums = [random.randint(0, 501) for _ in range(100_000)]

    # now = datetime.now()
    solve(nums)
    # print(datetime.now() - now)


if __name__ == '__main__':
    main()
