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.math.*;
  import java.util.*;
  import java.util.stream.*;
  import java.lang.management.*;
  import static java.lang.Math.*;
  
  @SuppressWarnings("unchecked")
  public class P1598C {
  
    public void run() throws Exception {
  nextT:
      for (int T = nextInt(); T > 0; T--) {
        long n = nextInt(), s = 0, ans = 0;
        Map<Long, Long> ac = new LinkedHashMap<>();
  
        for (int i = 0; i < n; i++) {
          long a = nextInt();
          s += a;
          ac.put(a, ac.getOrDefault(a, 0L) + 1);
        }
  
        long d = 2 * s / n;
  
        if ((d * n) == (2 * s)) {
          for (Map.Entry<Long, Long> me : ac.entrySet()) {
             long a = me.getKey(), b = d - a;
  
             if (b != a) {
               ans += me.getValue() * ac.getOrDefault(b, 0L);
             } else if (b == a) {
               ans += me.getValue() * (me.getValue() - 1);
             }
          }
        }
  
        println(ans >>> 1);
      }
    }
  
    public static void main(String... args) throws Exception {
      br = new BufferedReader(new InputStreamReader(System.in));
      pw = new PrintWriter(new BufferedOutputStream(System.out));
      new P1598C().run();
      br.close();
      pw.close();
      System.err.println("\n[Time : " + (System.currentTimeMillis() - startTime) + " ms]");
      long gct = 0, gcc = 0;
      for (GarbageCollectorMXBean garbageCollectorMXBean : ManagementFactory.getGarbageCollectorMXBeans()) {
        gct += garbageCollectorMXBean.getCollectionTime();
        gcc += garbageCollectorMXBean.getCollectionCount();
      }
      System.err.println("[GC time : " + gct + " ms, count = " + gcc + "]");
      System.err.println("[JIT time : " + ManagementFactory.getCompilationMXBean().getTotalCompilationTime() + " ms]");
    }
  
    static long startTime = System.currentTimeMillis();
    static BufferedReader br;
    static PrintWriter pw;
    StringTokenizer stok;
  
    String nextToken() throws IOException {
      while (stok == null || !stok.hasMoreTokens()) {
        String s = br.readLine();
        if (s == null) { return null; }
        stok = new StringTokenizer(s);
      }
      return stok.nextToken();
    }
  
    void print(byte b) { print("" + b); }
    void print(int i) { print("" + i); }
    void print(long l) { print("" + l); }
    void print(double d) { print("" + d); }
    void print(char c) { print("" + c); }
    void print(Object o) {
      if (o instanceof int[]) { print(Arrays.toString((int [])o));
      } else if (o instanceof long[]) { print(Arrays.toString((long [])o));
      } else if (o instanceof char[]) { print(Arrays.toString((char [])o));
      } else if (o instanceof byte[]) { print(Arrays.toString((byte [])o));
      } else if (o instanceof short[]) { print(Arrays.toString((short [])o));
      } else if (o instanceof boolean[]) { print(Arrays.toString((boolean [])o));
      } else if (o instanceof float[]) { print(Arrays.toString((float [])o));
      } else if (o instanceof double[]) { print(Arrays.toString((double [])o));
      } else if (o instanceof Object[]) { print(Arrays.toString((Object [])o));
      } else { print("" + o); }
    }
    void printsp(int [] a) { for (int i = 0, n = a.length; i < n; print(a[i] + " "), i++); }
    void printsp(long [] a) { for (int i = 0, n = a.length; i < n; print(a[i] + " "), i++); }
    void print(String s) { pw.print(s); }
    void println() { println(""); }
    void println(byte b) { println("" + b); }
    void println(int i) { println("" + i); }
    void println(long l) { println("" + l); }
    void println(double d) { println("" + d); }
    void println(char c) { println("" + c); }
    void println(Object o) { print(o); println(); }
    void println(String s) { pw.println(s); }
    int nextInt() throws IOException { return Integer.parseInt(nextToken()); }
    long nextLong() throws IOException { return Long.parseLong(nextToken()); }
    double nextDouble() throws IOException { return Double.parseDouble(nextToken()); }
    char nextChar() throws IOException { return (char) (br.read()); }
    String next() throws IOException { return nextToken(); }
    String nextLine() throws IOException { return br.readLine(); }
    int [] readInt(int size) throws IOException {
      int [] array = new int [size];
      for (int i = 0; i < size; i++) { array[i] = nextInt(); }
      return array;
    }
    long [] readLong(int size) throws IOException {
      long [] array = new long [size];
      for (int i = 0; i < size; i++) { array[i] = nextLong(); }
      return array;
    }
    double [] readDouble(int size) throws IOException {
      double [] array = new double [size];
      for (int i = 0; i < size; i++) { array[i] = nextDouble(); }
      return array;
    }
    String [] readLines(int size) throws IOException {
      String [] array = new String [size];
      for (int i = 0; i < size; i++) { array[i] = nextLine(); }
      return array;
    }
  
    int gcd(int a, int b) {
      if (a == 0) return Math.abs(b); if (b == 0) return Math.abs(a);
      a = Math.abs(a); b = Math.abs(b);
      int az = Integer.numberOfTrailingZeros(a), bz = Integer.numberOfTrailingZeros(b);
      a >>>= az; b >>>= bz;
      while (a != b) {
        if (a > b) { a -= b; a >>>= Integer.numberOfTrailingZeros(a); }
              else { b -= a; b >>>= Integer.numberOfTrailingZeros(b); }
      }
      return (a << Math.min(az, bz));
    }
  
    long gcd(long a, long b) {
      if (a == 0) return Math.abs(b); if (b == 0) return Math.abs(a);
      a = Math.abs(a); b = Math.abs(b);
      int az = Long.numberOfTrailingZeros(a), bz = Long.numberOfTrailingZeros(b);
      a >>>= az; b >>>= bz;
      while (a != b) {
        if (a > b) { a -= b; a >>>= Long.numberOfTrailingZeros(a); }
              else { b -= a; b >>>= Long.numberOfTrailingZeros(b); }
      }
      return (a << Math.min(az, bz));
    }
  
    boolean isPrime(int v) {
      if (v <= 1) { return false; }
      if (v <= 3) { return true; }
      if (((v & 1) == 0) || ((v % 3) == 0)) { return false; }
      for (int m = 5, n = (int)sqrt(v); m <= n; m += 6) { if (((v % m) == 0) || ((v % (m + 2)) == 0)) { return false; } }
      return true;
    }
  
    int [] rshuffle(int [] a) { // RANDOM shuffle
      Random r = new Random();
      for (int i = a.length - 1, j, t; i >= 0; j = r.nextInt(a.length), t = a[i], a[i] = a[j], a[j] = t, i--);
      return a;
    }
  
    int [] qshuffle(int [] a) { // QUICK shuffle
      int m = new Random().nextInt(10) + 2;
      for (int i = 0, n = a.length, j = m % n, t; i < n; t = a[i], a[i] = a[j], a[j] = t, i++, j = (i * m) % n);
      return a;
    }
  
    long [] shuffle(long [] a) {
      Random r = new Random();
      for (int i = a.length - 1; i >= 0; i--) {
        int j = r.nextInt(a.length);
        long t = a[i]; a[i] = a[j]; a[j] = t;
      }
      return a;
    }
  
    void shuffle(Object [] a) {
      Random r = new Random();
      for (int i = a.length - 1; i >= 0; i--) {
        int j = r.nextInt(a.length);
        Object t = a[i]; a[i] = a[j]; a[j] = t;
      }
    }
  
    int [] sort(int [] a) {
      final int SHIFT = 16, MASK = (1 << SHIFT) - 1, SIZE = (1 << SHIFT) + 1;
      int n = a.length, ta [] = new int [n], ai [] = new int [SIZE];
      for (int i = 0; i < n; ai[(a[i] & MASK) + 1]++, i++);
      for (int i = 1; i < SIZE; ai[i] += ai[i - 1], i++);
      for (int i = 0; i < n; ta[ai[a[i] & MASK]++] = a[i], i++);
      int [] t = a; a = ta; ta = t;
      ai = new int [SIZE];
      for (int i = 0; i < n; ai[(a[i] >> SHIFT) + 1]++, i++);
      for (int i = 1; i < SIZE; ai[i] += ai[i - 1], i++);
      for (int i = 0; i < n; ta[ai[a[i] >> SHIFT]++] = a[i], i++);
      return ta;
    }
  
    boolean nextPerm(int [] a) {
      int j, i = a.length - 2;
      for (; (i >= 0) && (a[i] > a[i + 1]); i--);
      if (i >= 0) {
        for (j = a.length - 1; a[i] > a[j]; j--);
        a[i] ^= a[j]; a[j] ^= a[i]; a[i] ^= a[j]; // swap(a[i], a[j])
        for (int l = i + 1, r = a.length - 1; l < r; l++, r--) {
          a[l] ^= a[r]; a[r] ^= a[l]; a[l] ^= a[r]; // swap(a[r], a[l])
        }
      }
      return (i >= 0);
    }
  
    void flush() {
      pw.flush();
    }
  
    void pause() {
      flush(); System.console().readLine();
    }
  }