Good Prefixes
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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 $3$.