Good Prefixes
Description
Alex thinks some array is good if there exists some element that can be represented as the sum of all other elements (the sum of all other elements is $0$ if there are no other elements). For example, the array $[1,6,3,2]$ is good since $1+3+2=6$. Furthermore, the array $[0]$ is also good. However, the arrays $[1,2,3,4]$ and $[1]$ are not good.
Alex has an array $a_1,a_2,\ldots,a_n$. Help him count the number of good non-empty prefixes of the array $a$. In other words, count the number of integers $i$ ($1 \le i \le n$) such that the length $i$ prefix (i.e. $a_1,a_2,\ldots,a_i$) is good.
The first line of the input contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of elements in the array.
The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($0 \le a_i \le 10^9$) — the elements of the array.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
For each test case, output a single integer — the number of good non-empty prefixes of the array $a$.
Input
The first line of the input contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of elements in the array.
The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($0 \le a_i \le 10^9$) — the elements of the array.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
Output
For each test case, output a single integer — the number of good non-empty prefixes of the array $a$.
7
1
0
1
1
4
1 1 2 0
5
0 1 2 1 4
7
1 1 0 3 5 2 12
7
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 294967296
10
0 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 589934592
1
0
3
3
4
1
2
Note
In the fourth test case, the array has five prefixes:
- prefix $[0]$ is a good array, as mentioned in the statement;
- prefix $[0, 1]$ is not a good array, since $0 \ne 1$;
- prefix $[0, 1, 2]$ is not a good array, since $0 \ne 1 + 2$, $1 \ne 0 + 2$ and $2 \ne 0 + 1$;
- prefix $[0, 1, 2, 1]$ is a good array, since $2 = 0 + 1 + 1$;
- prefix $[0, 1, 2, 1, 4]$ is a good array, since $4 = 0 + 1 + 2 + 1$.
As you can see, three of them are good, so the answer is $3$.