#P1582B. Luntik and Subsequences
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ID: 6106
Type: RemoteJudge
1000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Luntik and Subsequences
No submission language available for this problem.
Description
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.
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.
Samples
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
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 $0$).