description: 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.
solution: import java.io.*;
  import java.util.*;
  
  public class Trial {
  
      public static void main(String[] args) throws IOException {
  
          Scanner sc = new Scanner(System.in);
          PrintWriter pw = new PrintWriter(System.out);
  
          int q = sc.nextInt();
  
          while (q-- > 0) {
              int n = sc.nextInt();
              int [] arr = new int[n];
              double sum = 0;
              HashMap<Integer, Integer> hm = new HashMap<>();
              for (int i = 0; i < n; i++) {
                  int k = sc.nextInt();
                  arr[i] = k;
                  hm.put(k, hm.getOrDefault(k, 0) + 1);
                  sum += k;
              }
              double avg = sum / n;
              // sum - x / n - 2 = avg
              double toFind = sum - avg * (n - 2);
              if (toFind % 1 != 0) {
                  pw.println(0);
                  continue;
              }
              long res = 0;
              for (int i = 0; i < n; i++) {
                  int abs = (int) toFind - arr[i];
                  if (hm.containsKey(abs)) {
                      Integer count = hm.get(abs);
                      if (abs  == arr[i]) {
                          res += count - 1;
                      } else {
                          res += count;
                      }
                  }
              }
  
              pw.println(res / 2);
  
  
          }
          pw.flush();
          pw.close();
      }
  
      static class Scanner {
          StringTokenizer st;
          BufferedReader br;
  
          public Scanner(InputStream System) throws FileNotFoundException {
              br = new BufferedReader(new InputStreamReader(System));
          }
  
          public String next() throws IOException {
              while (st == null || !st.hasMoreTokens())
                  st = new StringTokenizer(br.readLine());
              return st.nextToken();
          }
  
          public String nextLine() throws IOException {
              return br.readLine();
          }
  
          public int nextInt() throws IOException {
              return Integer.parseInt(next());
          }
  
          public double nextDouble() throws IOException {
              return Double.parseDouble(next());
          }
  
          public char nextChar() throws IOException {
              return next().charAt(0);
          }
  
          public Long nextLong() throws IOException {
              return Long.parseLong(next());
          }
  
          public boolean ready() throws IOException {
              return br.ready();
          }
  
          public void waitForInput() {
              for (long i = 0; i < 3e9; i++)
                  ;
          }
      }
  
      static class Pair {
          int a;
          int b;
          boolean asc;
  
          Pair(int a, int b, boolean asc) {
              this.a = a;
              this.b = b;
              this.asc = asc;
          }
  
          @Override
          public boolean equals(Object o) {
              if (this == o) return true;
              if (o == null || getClass() != o.getClass()) return false;
              Pair pair = (Pair) o;
              return a == pair.a &&
                      b == pair.b &&
                      asc == pair.asc;
          }
  
          @Override
          public int hashCode() {
              return Objects.hash(a, b, asc);
          }
      }
  }
  