#P1985C. Good Prefixes

Good Prefixes

No submission language available for this problem.

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 00 if there are no other elements). For example, the array [1,6,3,2][1,6,3,2] is good since 1+3+2=61+3+2=6. Furthermore, the array [0][0] is also good. However, the arrays [1,2,3,4][1,2,3,4] and [1][1] are not good.

Alex has an array a1,a2,…,ana_1,a_2,\ldots,a_n. Help him count the number of good non-empty prefixes of the array aa. In other words, count the number of integers ii (1≤i≤n1 \le i \le n) such that the length ii prefix (i.e. a1,a2,…,aia_1,a_2,\ldots,a_i) is good.

The first line of the input contains a single integer tt (1≤t≤1041 \leq t \leq 10^4) — the number of test cases.

The first line of each test case contains a single integer nn (1≤n≤2⋅1051 \le n \le 2 \cdot 10^5) — the number of elements in the array.

The second line of each test case contains nn integers a1,a2,…,ana_1,a_2,\ldots,a_n (0≤ai≤1090 \le a_i \le 10^9) — the elements of the array.

It is guaranteed that the sum of nn over all test cases does not exceed 2⋅1052 \cdot 10^5.

For each test case, output a single integer — the number of good non-empty prefixes of the array aa.

Input

The first line of the input contains a single integer tt (1≤t≤1041 \leq t \leq 10^4) — the number of test cases.

The first line of each test case contains a single integer nn (1≤n≤2⋅1051 \le n \le 2 \cdot 10^5) — the number of elements in the array.

The second line of each test case contains nn integers a1,a2,…,ana_1,a_2,\ldots,a_n (0≤ai≤1090 \le a_i \le 10^9) — the elements of the array.

It is guaranteed that the sum of nn over all test cases does not exceed 2⋅1052 \cdot 10^5.

Output

For each test case, output a single integer — the number of good non-empty prefixes of the array aa.

Sample Input 1

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
Copy

Sample Output 1

1
0
3
3
4
1
2
Copy

Note

In the fourth test case, the array has five prefixes:

  • prefix [0][0] is a good array, as mentioned in the statement;
  • prefix [0,1][0, 1] is not a good array, since 0≠10 \ne 1;
  • prefix [0,1,2][0, 1, 2] is not a good array, since 0≠1+20 \ne 1 + 2, 1≠0+21 \ne 0 + 2 and 2≠0+12 \ne 0 + 1;
  • prefix [0,1,2,1][0, 1, 2, 1] is a good array, since 2=0+1+12 = 0 + 1 + 1;
  • prefix [0,1,2,1,4][0, 1, 2, 1, 4] is a good array, since 4=0+1+2+14 = 0 + 1 + 2 + 1.

As you can see, three of them are good, so the answer is 33.

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