# Luntik and Subsequences solution codeforces

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 ($$s= \sum_{i=1}^{n} a_i$$$). 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 $$t$$$ ($$1 \le t \le 1000$$$) — the number of test cases. The next $$2 \cdot t$$$ 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 $$n$$$($$1 \le n \le 60$$$) — the length of the array.

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

Output

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

Example
input

Copy
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

Copy
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 $$0$$\$).