A14598 | Delete Two Elements

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

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

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

Your task is to calculate 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 $a$ ).

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 $2 \cdot 10^5$ .

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 $a$ ).