A14657. Luntik and Subsequences

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.

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 $a$ .

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

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 $0$ ).