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


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

public final class Main {

    static PrintWriter out = new PrintWriter(System.out);
    static FastReader in = new FastReader();
    static Pair[] moves = new Pair[]{new Pair(-1, 0), new Pair(1, 0), new Pair(0, -1), new Pair(0, 1)};
    static int mod = (int) (1e9 + 7);
    static int mod2 = 998244353;

    public static void main(String[] args) {
        int tt = i();
        while (tt-- > 0) {
            solve();
        }
        out.flush();
    }

    public static void solve() {
        int n = i();
        int[] arr = input(n);
        long sum = 0L;
        for (int x : arr) {
            sum += x;
        }
        double mean = sum / (double) n * 2;
        double floor = Math.floor(mean);
        long ans = 0;
        if (floor == mean) {
            int t = (int) floor;
            Arrays.sort(arr);
            int l = 0;
            int r = n - 1;
            while (l < r) {
                if (arr[l] + arr[r] > t) {
                    r--;
                } else if (arr[l] + arr[r] == t) {
                    int a = 1;
                    int b = 1;
                    while (l + 1 < r && arr[l + 1] == arr[l]) {
                        l++;
                        a++;
                    }
                    while (l < r - 1 && arr[r - 1] == arr[r]) {
                        r--;
                        b++;
                    }
                    if (arr[l] == arr[r]) {
                        int c = a + b;
                        ans += (long) c * (c - 1) / 2;
                    } else {
                        ans += (long) a * b;
                    }

                    l++;
                    r--;
                } else {
                    l++;
                }
            }
            out.println(ans);
        } else {
            out.println(0);
        }

    }


    static long[] pre(int[] a) {
        long[] pre = new long[a.length + 1];
        pre[0] = 0;
        for (int i = 0; i < a.length; i++) {
            pre[i + 1] = pre[i] + a[i];
        }
        return pre;
    }

    static void print(char A[]) {
        for (char c : A) {
            out.print(c);
        }
        out.println();
    }

    static void print(boolean A[]) {
        for (boolean c : A) {
            out.print(c + " ");
        }
        out.println();
    }

    static void print(int A[]) {
        for (int c : A) {
            out.print(c + " ");
        }
        out.println();
    }

    static void print(long A[]) {
        for (long i : A) {
            out.print(i + " ");
        }
        out.println();
    }

    static void print(List<Integer> A) {
        for (int a : A) {
            out.print(a + " ");
        }
    }

    static int i() {
        return in.nextInt();
    }

    static long l() {
        return in.nextLong();
    }

    static String s() {
        return in.nextLine();
    }

    static int[][] inputWithIdx(int N) {
        int A[][] = new int[N][2];
        for (int i = 0; i < N; i++) {
            A[i] = new int[]{i, in.nextInt()};
        }
        return A;
    }

    static int[] input(int N) {
        int A[] = new int[N];
        for (int i = 0; i < N; i++) {
            A[i] = in.nextInt();
        }
        return A;
    }

    static long[] inputLong(int N) {
        long A[] = new long[N];
        for (int i = 0; i < A.length; i++) {
            A[i] = in.nextLong();
        }
        return A;
    }

    static int GCD(int a, int b) {
        if (b == 0) {
            return a;
        } else {
            return GCD(b, a % b);
        }
    }

    static long GCD(long a, long b) {
        if (b == 0) {
            return a;
        } else {
            return GCD(b, a % b);
        }
    }

    static long LCM(int a, int b) {
        return (long) a / GCD(a, b) * b;
    }

    static long LCM(long a, long b) {
        return a / GCD(a, b) * b;
    }

    static void shuffleAndSort(int[] arr) {
        for (int i = 0; i < arr.length; i++) {
            int rand = (int) (Math.random() * arr.length);
            int temp = arr[rand];
            arr[rand] = arr[i];
            arr[i] = temp;
        }
        Arrays.sort(arr);
    }

    static void shuffleAndSort(int[][] arr, Comparator<? super int[]> comparator) {
        for (int i = 0; i < arr.length; i++) {
            int rand = (int) (Math.random() * arr.length);
            int[] temp = arr[rand];
            arr[rand] = arr[i];
            arr[i] = temp;
        }
        Arrays.sort(arr, comparator);
    }

    static void shuffleAndSort(long[] arr) {
        for (int i = 0; i < arr.length; i++) {
            int rand = (int) (Math.random() * arr.length);
            long temp = arr[rand];
            arr[rand] = arr[i];
            arr[i] = temp;
        }
        Arrays.sort(arr);
    }

    static boolean isPerfectSquare(double number) {
        double sqrt = Math.sqrt(number);
        return ((sqrt - Math.floor(sqrt)) == 0);
    }

    static void swap(int A[], int a, int b) {
        int t = A[a];
        A[a] = A[b];
        A[b] = t;
    }

    static long pow(long a, long b, int mod) {
        long pow = 1;
        long x = a;
        while (b != 0) {
            if ((b & 1) != 0) {
                pow = (pow * x) % mod;
            }
            x = (x * x) % mod;
            b /= 2;
        }
        return pow;
    }

    static long pow(long a, long b) {
        long pow = 1;
        long x = a;
        while (b != 0) {
            if ((b & 1) != 0) {
                pow *= x;
            }
            x = x * x;
            b /= 2;
        }
        return pow;
    }

    static long modInverse(long x, int mod) {
        return pow(x, mod - 2, mod);
    }

    static boolean isPrime(long N) {
        if (N <= 1) {
            return false;
        }
        if (N <= 3) {
            return true;
        }
        if (N % 2 == 0 || N % 3 == 0) {
            return false;
        }
        for (int i = 5; i * i <= N; i = i + 6) {
            if (N % i == 0 || N % (i + 2) == 0) {
                return false;
            }
        }
        return true;
    }

    public static String reverse(String str) {
        if (str == null) {
            return null;
        }
        return new StringBuilder(str).reverse().toString();
    }

    public static String repeat(char ch, int repeat) {
        if (repeat <= 0) {
            return "";
        }
        final char[] buf = new char[repeat];
        for (int i = repeat - 1; i >= 0; i--) {
            buf[i] = ch;
        }
        return new String(buf);
    }

    public static int[] manacher(String s) {
        char[] chars = s.toCharArray();
        int n = s.length();
        int[] d1 = new int[n];
        for (int i = 0, l = 0, r = -1; i < n; i++) {
            int k = (i > r) ? 1 : Math.min(d1[l + r - i], r - i + 1);
            while (0 <= i - k && i + k < n && chars[i - k] == chars[i + k]) {
                k++;
            }
            d1[i] = k--;
            if (i + k > r) {
                l = i - k;
                r = i + k;
            }
        }
        return d1;
    }

    public static int[] kmp(String s) {
        int n = s.length();
        int[] res = new int[n];
        for (int i = 1; i < n; ++i) {
            int j = res[i - 1];
            while (j > 0 && s.charAt(i) != s.charAt(j)) {
                j = res[j - 1];
            }
            if (s.charAt(i) == s.charAt(j)) {
                ++j;
            }
            res[i] = j;
        }
        return res;
    }
}

class Pair {

    int i, j;

    Pair(int i, int j) {
        this.i = i;
        this.j = j;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) {
            return true;
        }
        if (o == null || getClass() != o.getClass()) {
            return false;
        }
        Pair pair = (Pair) o;
        return i == pair.i && j == pair.j;
    }

    @Override
    public int hashCode() {
        return Objects.hash(i, j);
    }
}

class FastReader {

    BufferedReader br;
    StringTokenizer st;

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

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

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

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

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

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}

class Node {

    int data, open, close;

    Node() {
        this(0, 0, 0);
    }

    Node(int data, int open, int close) {
        this.data = data;
        this.open = open;
        this.close = close;
    }
}

class ST {

    int n;
    Node[] st;

    ST(int n) {
        this.n = n;
        st = new Node[4 * Integer.highestOneBit(n)];
    }

    void build(Node[] nodes) {
        build(0, 0, n - 1, nodes);
    }

    private void build(int id, int l, int r, Node[] nodes) {
        if (l == r) {
            st[id] = nodes[l];
            return;
        }
        int mid = (l + r) >> 1;
        build((id << 1) + 1, l, mid, nodes);
        build((id << 1) + 2, mid + 1, r, nodes);
        st[id] = comb(st[(id << 1) + 1], st[(id << 1) + 2]);
    }

    void update(int i, Node node) {
        update(0, 0, n - 1, i, node);
    }

    private void update(int id, int l, int r, int i, Node node) {
        if (i < l || r < i) {
            return;
        }
        if (l == r) {
            st[id] = node;
            return;
        }
        int mid = (l + r) >> 1;
        update((id << 1) + 1, l, mid, i, node);
        update((id << 1) + 2, mid + 1, r, i, node);
        st[id] = comb(st[(id << 1) + 1], st[(id << 1) + 2]);
    }

    Node get(int x, int y) {
        return get(0, 0, n - 1, x, y);
    }

    private Node get(int id, int l, int r, int x, int y) {
        if (x > r || y < l) {
            return new Node();
        }
        if (x <= l && r <= y) {
            return st[id];
        }
        int mid = (l + r) >> 1;
        return comb(get((id << 1) + 1, l, mid, x, y), get((id << 1) + 2, mid + 1, r, x, y));
    }

    Node comb(Node a, Node b) {
        if (a == null) {
            return b;
        }
        if (b == null) {
            return a;
        }
        int min = Math.min(a.open, b.close);
        return new Node(a.data + b.data + min * 2, a.open + b.open - min, a.close + b.close - min);
    }
}