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.
1
3
228 1337 228

0

//
// Source code recreated from a .class file by IntelliJ IDEA
// (powered by Fernflower decompiler)
//

import java.io.BufferedWriter;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.util.*;

public class CFC {
    static CFC.Reader sc = new CFC.Reader();
    static BufferedWriter bw;
    static int team1;
    static int team2;
    static int minkicks;

    public CFC() {
    }

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        process:
        for (int p = 0; p < t; p++) {
              int n=sc.nextInt();
              double avg=0;
              Map<Integer,Integer> map1=new HashMap<>();
              Map<Integer,Boolean> map2=new HashMap<>();
              for(int i=0;i<n;i++){
                  int num=sc.nextInt();
                  map1.putIfAbsent(num,0);
                  map1.put(num,map1.get(num)+1);
                  avg+=num;
                  map2.put(num,false);
              }
              //boolean flag=false;
              if(avg%n!=0){
                  System.out.println(0);
                  continue process;
              }
              avg/= n;
              avg*=2;
              long count=0;


              for(Integer integer:map1.keySet()){
                   int diff=(int)avg;
                   int d2=diff-integer;

                   if(!map2.get(integer) && map1.containsKey(d2)){
                       map2.put(integer,true);
                       map2.put(d2,true);
                       if(integer!=d2){
                           count+=(long)map1.get(integer)*map1.get(d2);
                       }else{
                           int c=map1.get(integer);
                           count+=((long)c*(c-1))/2;
                       }

                   }


              }
            System.out.println(count);


        }


        bw.flush();
        bw.close();
    }

    public static int checker(int a) {
        if (a % 2 == 0) {
            return 1;
        } else {
            byte b;
            do {
                b = 2;
            } while (a + b != (a ^ b));

            return b;
        }
    }

    public static boolean checkPrime(int n) {
        if (n != 0 && n != 1) {
            for (int j = 2; j * j <= n; ++j) {
                if (n % j == 0) {
                    return false;
                }
            }

            return true;
        } else {
            return false;
        }
    }

    public static void dfs1(List<List<Integer>> g, boolean[] visited, Stack<Integer> stack, int num) {
        visited[num] = true;
        Iterator var4 = ((List) g.get(num)).iterator();

        while (var4.hasNext()) {
            Integer integer = (Integer) var4.next();
            if (!visited[integer]) {
                dfs1(g, visited, stack, integer);
            }
        }

        stack.push(num);
    }

    public static void dfs2(List<List<Integer>> g, boolean[] visited, List<Integer> list, int num, int c, int[] raj) {
        visited[num] = true;
        Iterator var6 = ((List) g.get(num)).iterator();

        while (var6.hasNext()) {
            Integer integer = (Integer) var6.next();
            if (!visited[integer]) {
                dfs2(g, visited, list, integer, c, raj);
            }
        }

        raj[num] = c;
        list.add(num);
    }

    public static int inputInt() throws IOException {
        return sc.nextInt();
    }

    public static long inputLong() throws IOException {
        return sc.nextLong();
    }

    public static double inputDouble() throws IOException {
        return sc.nextDouble();
    }

    public static String inputString() throws IOException {
        return sc.readLine();
    }

    public static void print(String a) throws IOException {
        bw.write(a);
    }

    public static void printSp(String a) throws IOException {
        bw.write(a + " ");
    }

    public static void println(String a) throws IOException {
        bw.write(a + "\n");
    }

    public static long getAns(int[] ar, int c, long[][] dp, int i, int sign) {
        if (i < 0) {
            return 1L;
        } else if (c <= 0) {
            return 1L;
        } else {
            dp[i][c] = Math.max(dp[i][c], Math.max((long) ar[i] * getAns(ar, c - 1, dp, i - 1, sign), getAns(ar, c, dp, i - 1, 1)));
            return dp[i][c];
        }
    }

    public static long power(long a, long b, long c) {
        long ans;
        for (ans = 1L; b != 0L; b /= 2L) {
            if (b % 2L == 1L) {
                ans *= a;
                ans %= c;
            }

            a *= a;
            a %= c;
        }

        return ans;
    }

    public static long power1(long a, long b, long c) {
        long ans;
        for (ans = 1L; b != 0L; b /= 2L) {
            if (b % 2L == 1L) {
                ans = multiply(ans, a, c);
            }

            a = multiply(a, a, c);
        }

        return ans;
    }

    public static long multiply(long a, long b, long c) {
        long res = 0L;

        for (a %= c; b > 0L; b /= 2L) {
            if (b % 2L == 1L) {
                res = (res + a) % c;
            }

            a = (a + a) % c;
        }

        return res % c;
    }

    public static long totient(long n) {
        long result = n;

        for (long i = 2L; i * i <= n; ++i) {
            if (n % i == 0L) {
                while (n % i == 0L) {
                    n /= i;
                }

                result -= result / i;
            }
        }

        if (n > 1L) {
            result -= result / n;
        }

        return result;
    }

    public static long gcd(long a, long b) {
        return b == 0L ? a : gcd(b, a % b);
    }

    public static boolean[] primes(int n) {
        boolean[] p = new boolean[n + 1];
        p[0] = false;
        p[1] = false;

        int i;
        for (i = 2; i <= n; ++i) {
            p[i] = true;
        }

        for (i = 2; i * i <= n; ++i) {
            if (p[i]) {
                for (int j = i * i; j <= n; j += i) {
                    p[j] = false;
                }
            }
        }

        return p;
    }

    public String LargestEven(String S) {
        int[] count = new int[10];

        int num;
        for (num = 0; num < S.length(); ++num) {
            ++count[S.charAt(num) - 48];
        }

        num = -1;

        for (int i = 0; i <= 8; i += 2) {
            if (count[i] > 0) {
                num = i;
                break;
            }
        }

        StringBuilder ans = new StringBuilder();

        for (int i = 9; i >= 0; --i) {
            int j;
            if (i != num) {
                for (j = 1; j <= count[i]; ++j) {
                    ans.append(i);
                }
            } else {
                for (j = 1; j <= count[num] - 1; ++j) {
                    ans.append(num);
                }
            }
        }

        if (num != -1 && count[num] > 0) {
            ans.append(num);
        }

        return ans.toString();
    }

    static {
        bw = new BufferedWriter(new OutputStreamWriter(System.out));
        team1 = 0;
        team2 = 0;
        minkicks = 10;
    }

    public static class Score {
        int l;
        String s;

        public Score(int l, String s) {
            this.l = l;
            this.s = s;
        }
    }

    public static class Ath {
        int r1;
        int r2;
        int r3;
        int r4;
        int r5;
        int index;

        public Ath(int r1, int r2, int r3, int r4, int r5, int index) {
            this.r1 = r1;
            this.r2 = r2;
            this.r3 = r3;
            this.r4 = r4;
            this.r5 = r5;
            this.index = index;
        }
    }

    static class Reader {
        private final int BUFFER_SIZE = 65536;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer;
        private int bytesRead;

        public Reader() {
            this.din = new DataInputStream(System.in);
            this.buffer = new byte[65536];
            this.bufferPointer = this.bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            this.din = new DataInputStream(new FileInputStream(file_name));
            this.buffer = new byte[65536];
            this.bufferPointer = this.bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64];

            int cnt;
            byte c;
            for (cnt = 0; (c = this.read()) != -1 && c != 10; buf[cnt++] = (byte) c) {
            }

            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;

            byte c;
            for (c = this.read(); c <= 32; c = this.read()) {
            }

            boolean neg = c == 45;
            if (neg) {
                c = this.read();
            }

            do {
                ret = ret * 10 + c - 48;
            } while ((c = this.read()) >= 48 && c <= 57);

            return neg ? -ret : ret;
        }

        public long nextLong() throws IOException {
            long ret = 0L;

            byte c;
            for (c = this.read(); c <= 32; c = this.read()) {
            }

            boolean neg = c == 45;
            if (neg) {
                c = this.read();
            }

            do {
                ret = ret * 10L + (long) c - 48L;
            } while ((c = this.read()) >= 48 && c <= 57);

            return neg ? -ret : ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0.0D;
            double div = 1.0D;

            byte c;
            for (c = this.read(); c <= 32; c = this.read()) {
            }

            boolean neg = c == 45;
            if (neg) {
                c = this.read();
            }

            do {
                ret = ret * 10.0D + (double) c - 48.0D;
            } while ((c = this.read()) >= 48 && c <= 57);

            if (c == 46) {
                while ((c = this.read()) >= 48 && c <= 57) {
                    ret += (double) (c - 48) / (div *= 10.0D);
                }
            }

            return neg ? -ret : ret;
        }

        private void fillBuffer() throws IOException {
            this.bytesRead = this.din.read(this.buffer, this.bufferPointer = 0, 65536);
            if (this.bytesRead == -1) {
                this.buffer[0] = -1;
            }

        }

        private byte read() throws IOException {
            if (this.bufferPointer == this.bytesRead) {
                this.fillBuffer();
            }

            return this.buffer[this.bufferPointer++];
        }

        public void close() throws IOException {
            if (this.din != null) {
                this.din.close();
            }
        }
    }
}
