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

/**
 * 10/09/21 night
 * https://codeforces.com/contest/1598/problem/C
 */
// package codeforce.ecf.r115;

import java.util.*;
import java.io.*;

public class C {

    static PrintWriter pw;

    /**
     * 1 + 4 + 7 + 3 + 5 = 20/5 = 4
     * 4 + 3 + 5 = 12 / 3 = 4    1 + 7
     * 1 + 4 + 7 = 12 / 3 = 4    3 + 5
     */
    void solve(int n, int[] a) {
        // tr(n, a);
        // tr(20 % 2.5 == 0, 20 % 2.6 == 0);
        long sum = 0;
        Map<Integer, Integer> m = new HashMap<>();
        for (int x : a) {
            sum += x;
            m.put(x, m.getOrDefault(x, 0) + 1);
        }
        long res = 0;
        Set<String> se = new HashSet<>();
        for (int x : m.keySet()) {
            double t = (double) n / 2;
            int y = (int) (sum / t) - x;
            int xocc = m.get(x);
            String ke;
            if (x <= y) {
                ke = x + " " + y;
            } else {
                ke = y + " " + x;
            }
            if (se.contains(ke)) continue;
            if (x == y) {
                if (xocc >= 2) {
                    // tr(x, y);
                    res += combination(xocc, 2);
                    se.add(ke);
                }
            } else {
                if (m.containsKey(y)) {
                    // tr(x, y);
                    int yocc = m.get(y);
                    res += xocc * yocc;
                    se.add(ke);
                }
            }
        }
        pr(res);
    }

    long combination(long m, long n) {
        return factorial(m, n) / factorial(n, n);
    }

    long factorial(long m, long n) {
        long num = 1;
        long cnt = 0;
        for (long i = m; i > 0; i--) {
            if (cnt == n) break;
            num *= i;
            cnt++;
        }
        return num;
    }

    private void run() {
        // read_write_file(); // comment this before submission
        FastScanner fs = new FastScanner();
        int t = fs.nextInt();
        while (t-- > 0) {
            int n = fs.nextInt();
            int[] a = fs.readArray(n);
            solve(n, a);
        }
    }

    private final String INPUT = "input.txt";
    private final String OUTPUT = "output.txt";

    void read_write_file() {
        FileInputStream instream = null;
        PrintStream outstream = null;
        try {
            instream = new FileInputStream(INPUT);
            outstream = new PrintStream(new FileOutputStream(OUTPUT));
            System.setIn(instream);
            System.setOut(outstream);
        } catch (Exception e) {
        }
    }

    public static void main(String[] args) {
        pw = new PrintWriter(System.out);
        new C().run();
        pw.close();
    }

    void pr(int num) {
        pw.println(num);
    }

    void pr(long num) {
        pw.println(num);
    }

    void pr(double num) {
        pw.println(num);
    }

    void pr(String s) {
        pw.println(s);
    }

    void pr(char c) {
        pw.println(c);
    }

    class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        Integer[] readIntegerArray(int n) {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    void tr(Object... o) {
        pw.println(Arrays.deepToString(o));
    }
}
