Statement

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.

Format

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 $a$ .

Sample

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