Delete Two Elements

Description:

Input:

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

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

The second line contains a sequence of integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le 10^{9}$$$), where $$$a_i$$$ is the $$$i$$$-th element of the array.

The sum of $$$n$$$ over all testcases doesn't exceed $$$2 \cdot 10^5$$$.

Output:

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

Sample Input:

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:

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 $$$1$$$ and $$$3$$$, or the elements on positions $$$4$$$ and $$$5$$$.