#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T &x) {
  x = 0;
  bool f = false;
  char ch = getchar();
  while (!isdigit(ch)) {
    f |= ch == '-';
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + (ch ^ 48);
    ch = getchar();
  }
  x = f ? -x : x;
  return;
}
template <typename T>
inline void write(T x) {
  if (x < 0) x = -x, putchar('-');
  if (x > 9) write(x / 10);
  putchar(x % 10 ^ 48);
  return;
}
const int MOD = 1e9 + 7;
inline int inc(int x, int y) {
  x += y;
  return x >= MOD ? x - MOD : x;
}
inline int dec(int x, int y) {
  x -= y;
  return x < 0 ? x + MOD : x;
}
inline void incc(int &x, int y) {
  x += y;
  if (x >= MOD) x -= MOD;
}
inline void decc(int &x, int y) {
  x -= y;
  if (x < 0) x += MOD;
}
inline void chkmin(int &x, int y) {
  if (y < x) x = y;
}
inline void chkmax(int &x, int y) {
  if (y > x) x = y;
}
const int N = 2e5 + 5, M = 3005, INF = 1e9 + 7;
namespace Map {
const int Size = 1e6 + 5;
int head[Size], nex[Size], val[Size], idx, sta[Size], top;
int to[Size];
const int mod = 999983;
inline void Reset() {
  for (int i = 1; i <= top; i++) head[sta[i]] = 0;
  idx = 0;
  return;
}
inline void Insert(int x, int v) {
  int key = (x % mod * 131) % mod * 13 % mod;
  for (int i = head[key]; i; i = nex[i])
    if (to[i] == x) return val[i] += v, void();
  nex[++idx] = head[key], to[idx] = x, val[idx] = v, head[key] = idx;
  sta[++top] = key;
  return;
}
inline int Count(int x) {
  int key = (x % mod * 131) % mod * 13 % mod;
  for (int i = head[key]; i; i = nex[i])
    if (to[i] == x) return val[i];
  return 0;
}
}  // namespace Map
int n, m, a[N];
signed main() {
  int t;
  read(t);
  while (t--) {
    read(n);
    Map::Reset();
    double sum = 0;
    for (register int i = (1); i <= (n); i++)
      read(a[i]), Map::Insert(a[i], 1), sum += (double)a[i];
    sum = sum * 1.0 / (n * 1.0);
    sum *= 2.0;
    if (floor(sum) != sum)
      puts("0");
    else {
      int tmp = sum;
      long long Ans = 0;
      for (int i = 1; i <= n; i++) {
        if (a[i] + a[i] < tmp) Ans += Map::Count(tmp - a[i]);
      }
      if (!(tmp & 1)) {
        int tp = Map::Count(tmp / 2);
        Ans += 1ll * tp * (tp - 1) / 2;
      }
      write(Ans), putchar('\n');
    }
  }
  return 0;
}

### Prompt

Your task is to create a Cpp solution to the following problem:

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).

Input

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

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

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

The sum of n over all testcases doesn't exceed 2 ⋅ 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).

Example

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


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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T &x) {
  x = 0;
  bool f = false;
  char ch = getchar();
  while (!isdigit(ch)) {
    f |= ch == '-';
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + (ch ^ 48);
    ch = getchar();
  }
  x = f ? -x : x;
  return;
}
template <typename T>
inline void write(T x) {
  if (x < 0) x = -x, putchar('-');
  if (x > 9) write(x / 10);
  putchar(x % 10 ^ 48);
  return;
}
const int MOD = 1e9 + 7;
inline int inc(int x, int y) {
  x += y;
  return x >= MOD ? x - MOD : x;
}
inline int dec(int x, int y) {
  x -= y;
  return x < 0 ? x + MOD : x;
}
inline void incc(int &x, int y) {
  x += y;
  if (x >= MOD) x -= MOD;
}
inline void decc(int &x, int y) {
  x -= y;
  if (x < 0) x += MOD;
}
inline void chkmin(int &x, int y) {
  if (y < x) x = y;
}
inline void chkmax(int &x, int y) {
  if (y > x) x = y;
}
const int N = 2e5 + 5, M = 3005, INF = 1e9 + 7;
namespace Map {
const int Size = 1e6 + 5;
int head[Size], nex[Size], val[Size], idx, sta[Size], top;
int to[Size];
const int mod = 999983;
inline void Reset() {
  for (int i = 1; i <= top; i++) head[sta[i]] = 0;
  idx = 0;
  return;
}
inline void Insert(int x, int v) {
  int key = (x % mod * 131) % mod * 13 % mod;
  for (int i = head[key]; i; i = nex[i])
    if (to[i] == x) return val[i] += v, void();
  nex[++idx] = head[key], to[idx] = x, val[idx] = v, head[key] = idx;
  sta[++top] = key;
  return;
}
inline int Count(int x) {
  int key = (x % mod * 131) % mod * 13 % mod;
  for (int i = head[key]; i; i = nex[i])
    if (to[i] == x) return val[i];
  return 0;
}
}  // namespace Map
int n, m, a[N];
signed main() {
  int t;
  read(t);
  while (t--) {
    read(n);
    Map::Reset();
    double sum = 0;
    for (register int i = (1); i <= (n); i++)
      read(a[i]), Map::Insert(a[i], 1), sum += (double)a[i];
    sum = sum * 1.0 / (n * 1.0);
    sum *= 2.0;
    if (floor(sum) != sum)
      puts("0");
    else {
      int tmp = sum;
      long long Ans = 0;
      for (int i = 1; i <= n; i++) {
        if (a[i] + a[i] < tmp) Ans += Map::Count(tmp - a[i]);
      }
      if (!(tmp & 1)) {
        int tp = Map::Count(tmp / 2);
        Ans += 1ll * tp * (tp - 1) / 2;
      }
      write(Ans), putchar('\n');
    }
  }
  return 0;
}

```