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

//package MyPackage;
import java.io.*;
import java.util.*;

public class MyClass {
    final static long mod = 1_000_000_007;
    final static int mini = Integer.MIN_VALUE;
    final static int maxi = Integer.MAX_VALUE;
    static int lb(int[] arr, int l, int h, int x) {
        while (l < h) {
            int mid = l + (h - l) / 2;
            if (arr[mid] >= x) h = mid;
            else l = mid + 1;
        }
        return l;
    }
    static int ub(int[] arr, int l, int h, int x) {
        while (l < h) {
            int mid = l + (h - l) / 2;
            if (arr[mid] > x) h = mid;
            else l = mid + 1;
        }
        return l;
    }
    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
    static long ncr(long n, long r) {
        if (r > n - r) r = n - r;
        long[] C = new long[(int) r + 1];
        C[0] = 1;
        for (int i = 1; i <= n; i++) {
            for (long j = Math.min(i, r); j > 0; j--)
                C[(int) j] = (C[(int) j] + C[(int) j - 1]) % mod;
        }
        return C[(int) r];
    }
    static boolean isPrime(long n) {
        if (n <= 1)
            return false;
        else if (n == 2)
            return true;
        else if (n % 2 == 0)
            return false;
        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            if (n % i == 0)
                return false;
        }
        return true;
    }
    static boolean isPalindrome(String s) {
        int i = 0, j = s.length() - 1;
        while(i < j) {
            if(s.charAt(i) != s.charAt(j)) return false;
            i++;
            j--;
        }
        return true;
    }
    static long lcm(long a, long b) {
        return (a / gcd(a, b)) * b;
    }
    static void sort(long[] a) {
        ArrayList<Long> l = new ArrayList<>();
        for (long value : a) {
            l.add(value);
        }
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a[i] = l.get(i);
    }
    static int ceil(int a, int b) {
        return a % b == 0 ? a / b : a / b + 1;
    }
    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int value : a) {
            l.add(value);
        }
        Collections.sort(l);
        for (int i = 0; i < l.size(); i++)
            a[i] = l.get(i);
    }
    static void reverse(int[] arr) {
        int l = 0;
        int h = arr.length - 1;
        while (l < h) {
            swap(arr, l, h);
            l++;
            h--;
        }
    }
    static String reverse(String s) {
        StringBuilder res = new StringBuilder(s);
        return res.reverse().toString();
    }
    static void swap(int[] arr, int i, int j) {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String n() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nint() {
            return Integer.parseInt(n());
        }

        long nlong() {
            return Long.parseLong(n());
        }

        double ndouble() {
            return Double.parseDouble(n());
        }

        int[] narr(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nint();
            return a;
        }
        int[][] narr(int n, int m) {
            int[][] a = new int[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    a[i][j] = nint();
            return a;
        }

        String nline() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    static class Pair implements Comparable<Pair> {
        int a, b;
        Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }
        public int compareTo(Pair p) {
            return -Integer.compare(a, p.a);
        }
    }
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        // int t = 1;
        int t = sc.nint();
        while(t-- > 0) {
            int n = sc.nint();
            int[] arr = sc.narr(n);
            sort(arr);
            double sum = 0;
            long count = 0;
            for(int i : arr) sum += i;
            sum /= n;
            if(sum % 1 == 0 || sum % 1 == 0.5) {
                int ts = (int) (sum * 2);
                for(int i = 0; i < n; i++) {
                    int x = ts - arr[i];
                    if(x >= 0) {
                        count += ub(arr, i + 1, n, x);
                        count -= lb(arr, i + 1, n, x);
                    }
                }
                out.println(count);
            }
            else {
                out.println(0);
            }
        }
        out.flush();
        out.close();
    }
}