#P1598C. Delete Two Elements

    ID: 288 Type: RemoteJudge 2000ms 256MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>data structuresdpimplementationmathtwo pointers*1200

Delete Two Elements

No submission language available for this problem.

Description

Monocarp has got an array aa consisting of nn integers. Let's denote kk as the mathematic mean of these elements (note that it's possible that kk is not an integer).

The mathematic mean of an array of nn elements is the sum of elements divided by the number of these elements (i. e. sum divided by nn).

Monocarp wants to delete exactly two elements from aa so that the mathematic mean of the remaining (n2)(n - 2) elements is still equal to kk.

Your task is to calculate the number of pairs of positions [i,j][i, j] (i<ji < j) such that if the elements on these positions are deleted, the mathematic mean of (n2)(n - 2) remaining elements is equal to kk (that is, it is equal to the mathematic mean of nn elements of the original array aa).

The first line contains a single integer tt (1t1041 \le t \le 10^4) — the number of testcases.

The first line of each testcase contains one integer nn (3n21053 \le n \le 2 \cdot 10^5) — the number of elements in the array.

The second line contains a sequence of integers a1,a2,,ana_1, a_2, \dots, a_n (0ai1090 \le a_i \le 10^{9}), where aia_i is the ii-th element of the array.

The sum of nn over all testcases doesn't exceed 21052 \cdot 10^5.

Print one integer — the number of pairs of positions [i,j][i, j] (i<ji < j) such that if the elements on these positions are deleted, the mathematic mean of (n2)(n - 2) remaining elements is equal to kk (that is, it is equal to the mathematic mean of nn elements of the original array aa).

Input

The first line contains a single integer tt (1t1041 \le t \le 10^4) — the number of testcases.

The first line of each testcase contains one integer nn (3n21053 \le n \le 2 \cdot 10^5) — the number of elements in the array.

The second line contains a sequence of integers a1,a2,,ana_1, a_2, \dots, a_n (0ai1090 \le a_i \le 10^{9}), where aia_i is the ii-th element of the array.

The sum of nn over all testcases doesn't exceed 21052 \cdot 10^5.

Output

Print one integer — the number of pairs of positions [i,j][i, j] (i<ji < j) such that if the elements on these positions are deleted, the mathematic mean of (n2)(n - 2) remaining elements is equal to kk (that is, it is equal to the mathematic mean of nn elements of the original array aa).

Samples

Sample Input 1

4
4
8 8 8 8
3
50 20 10
5
1 4 7 3 5
7
1 2 3 4 5 6 7

Sample Output 1

6
0
2
3

Note

In the first example, any pair of elements can be removed since all of them are equal.

In the second example, there is no way to delete two elements so the mathematic mean doesn't change.

In the third example, it is possible to delete the elements on positions 11 and 33, or the elements on positions 44 and 55.