Luntik and Subsequences

题意翻译

### 题目描述 有一个长度为 $n$ 的序列 $a_1,a_2,\dots,a_n$，和为 $s$，求这个序列有多少个子序列（可以为空）和为 $s-1$。 ### 输入格式 第一行输入一个正整数 $t$ 表示数据组数。 接下来 $2t$ 行每 $2$ 行表示一组数据。 对于每组数据，第一行输入一个正整数 $n$ 表示序列长度；第二行输入 $n$ 个整数表示这个序列。 ### 输出格式 对于每组数据，输出一行一个整数表示满足条件的子序列的个数。 ### 数据范围 $1\le t\le1000,1\le n\le60,0\le a_i\le10^9$。 ### 样例解释 第一组数据，满足条件的子序列为 $\{2,3,4,5\}$。 第二组数据，没有满足条件的子序列。 第三组数据，满足条件的子序列为 $\{\}$ 和 $\{0\}$。

题目描述

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.

输入输出格式

输入格式

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 $ .

输出格式

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

输入输出样例

输入样例 #1

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

输出样例 #1

1
0
2
4
4

说明

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 $ ).