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: // Author : RegalBeast
  
  import java.io.*;
  import java.util.*;
  import java.util.concurrent.*;
  
  public class Main implements Runnable {
    static Input in = new Input();
    static PrintWriter out = Output();
    
    public static void main(String[] args) {
      new Thread(null, new Main(), String.join(
                                    "All that is gold does not glitter,",
                                    "Not all those who wander are lost;",
                                    "The old that is strong does not wither,",
                                    "Deep roots are not reached by the frost.",
                                    
                                    "From the ashes a fire shall be woken,",
                                    "A light from the shadows shall spring;",
                                    "Renewed shall be blade that was broken,",
                                    "The crownless again shall be king."
                                  ), 1<<25).start();
    }
  
    public void run() {
      int tests = in.nextInt();
      for (int t = 0; t < tests; t++) {
        int n = in.nextInt();
        Map<Integer, Integer> freq = new HashMap<Integer, Integer>();
  
        long sum = 0;
        for (int i = 0; i < n; i++) {
          int ai = in.nextInt();
          sum += ai;
  
          if (!freq.containsKey(ai)) {
            freq.put(ai, 0);
          }
          freq.put(ai, freq.get(ai)+1);
        }
  
        long pairs = countPairs(n, sum, freq);
        out.println(pairs);
      }
      
      in.close();
      out.close();
    }
  
    static long countPairs(int n, long sum, Map<Integer, Integer> freq) {
      long pairs = 0;
  
      for (var me : freq.entrySet()) {
        int a = me.getKey();
        int b = getB(a, n, sum);
        // out.println(b);
        if (b == -1) {
          continue;
        }
  
        int aCount = me.getValue();
        Integer bCount = freq.get(b);
        if (bCount == null) {
          continue;
        }
  
        if (a == b) {
          pairs += (long) aCount * (aCount-1) / 2;
        } else {
          pairs += (long) aCount * bCount;
          freq.put(b, 0);
        }
        freq.put(a, 0);
      }
  
      return pairs;
    }
  
    static int getB(int a, int n, long sum) {
      // out.println(a + " " + n + " s" + sum);
      long rem = 2 * sum - (long) n * a;
      if (rem < 0 || rem % n > 0) {
        return -1;
      }
  
      return (int) (rem / n);
    }
    
    static PrintWriter Output() {
      return new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    }
    
    static PrintWriter Output(String fileName) {
      PrintWriter pw = null;
      try {
        pw = new PrintWriter(new BufferedWriter(new FileWriter(fileName)));
      } catch (IOException ex) {
        ex.printStackTrace();
      }
      return pw;
    }
  }
  
  class Input {
    BufferedReader br;
    StringTokenizer st;
    public Input() {
      br = new BufferedReader(new InputStreamReader(System.in));
    }
  
    public Input(String fileName) {
      try {
        br = new BufferedReader(new FileReader(fileName));
      } catch (IOException ex) {
        ex.printStackTrace();
      }
    }
  
    public String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          st = new StringTokenizer(br.readLine());
        } catch (IOException ex) {
          ex.printStackTrace();
        }
      }
      return st.nextToken();
    }
  
    public int nextInt() {
      return Integer.parseInt(next());
    }
  
    public long nextLong() {
      return Long.parseLong(next());
    }
  
    public Float nextFloat() {
      return Float.parseFloat(next());
    }
  
    public Double nextDouble() {
      return Double.parseDouble(next());
    }
  
    public String nextLine() {
      if (st != null && st.hasMoreElements()) {
        StringBuilder sb = new StringBuilder();
        while (st.hasMoreElements()) {
          sb.append(next());
        }
        return sb.toString();
      }
  
      String str = null;
      try {
        str = br.readLine();
      } catch (IOException ex) {
        ex.printStackTrace();
      }
      return str;
    }
  
    public void close() {
      try {
        br.close();
      } catch (IOException ex) {
        ex.printStackTrace();
      }
    }
  }
  