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

public class Main {

    static long startTime = System.currentTimeMillis();

    // for global initializations and methods starts here

    // global initialisations and methods end here

    static void run() {
        boolean tc = true;
        AdityaFastIO r = new AdityaFastIO();
        //FastReader r = new FastReader();

        try (OutputStream out = new BufferedOutputStream(System.out)) {

            //long startTime = System.currentTimeMillis();

            int testcases = tc ? r.ni() : 1;
            int tcCounter = 1;
            // Hold Here Sparky------------------->>>
            // Solution Starts Here

            start:
            while (testcases-- > 0) {

                int n = r.ni();

                long[] arr = new long[n];
                for (int i = 0; i < n; i++) arr[i] = r.nl();

                long sum = Arrays.stream(arr).sum();
                sum <<= 1;
                boolean ff = false;
                long get = 0;
                if (sum % n != 0) ff = true;
                else {
                    Map<Long, Long> map = new HashMap<>();
                    sum /= n;
                    int i = 0;
                    while (i < n) {
                        long diff = sum - arr[i];
                        get += map.getOrDefault(diff, 0L);
                        map.put(arr[i], map.getOrDefault(arr[i], 0L) + 1);
                        i++;
                    }
                }

                if (ff) out.write((0 + " ").getBytes());
                else out.write((get + " ").getBytes());
                out.write(("\n").getBytes());
            }
            // Solution Ends Here
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    static class AdityaFastIO {
        final private int BUFFER_SIZE = 1 << 16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;
        public BufferedReader br;
        public StringTokenizer st;

        public AdityaFastIO() {
            br = new BufferedReader(new InputStreamReader(System.in));
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public AdityaFastIO(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

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

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

        public String readLine() throws IOException {
            byte[] buf = new byte[100000001]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int ni() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public long nl() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public double nd() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (c == '.') while ((c = read()) >= '0' && c <= '9') ret += (c - '0') / (div *= 10);
            if (neg) return -ret;
            return ret;
        }

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

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) fillBuffer();
            return buffer[bufferPointer++];
        }

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

    public static void main(String[] args) throws Exception {
        run();
    }

    static long mod = 998244353;

    static long modInv(long base, long e) {
        long result = 1;
        base %= mod;
        while (e > 0) {
            if ((e & 1) > 0) result = result * base % mod;
            base = base * base % mod;
            e >>= 1;
        }
        return result;
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

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

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

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

        int ni() {
            return Integer.parseInt(word());
        }

        long nl() {
            return Long.parseLong(word());
        }

        double nd() {
            return Double.parseDouble(word());
        }
    }

    static int MOD = (int) (1e9 + 7);

    static long powerLL(long x, long n) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 1) result = result * x % MOD;
            n = n / 2;
            x = x * x % MOD;
        }
        return result;
    }

    static long powerStrings(int i1, int i2) {
        String sa = String.valueOf(i1);
        String sb = String.valueOf(i2);
        long a = 0, b = 0;
        for (int i = 0; i < sa.length(); i++) a = (a * 10 + (sa.charAt(i) - '0')) % MOD;
        for (int i = 0; i < sb.length(); i++) b = (b * 10 + (sb.charAt(i) - '0')) % (MOD - 1);
        return powerLL(a, b);
    }

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

    static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    static long lower_bound(int[] arr, int x) {
        int l = -1, r = arr.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (arr[m] >= x) r = m;
            else l = m;
        }
        return r;
    }

    static int upper_bound(int[] arr, int x) {
        int l = -1, r = arr.length;
        while (l + 1 < r) {
            int m = (l + r) >>> 1;
            if (arr[m] <= x) l = m;
            else r = m;
        }
        return l + 1;
    }

    static void addEdge(ArrayList<ArrayList<Integer>> graph, int edge1, int edge2) {
        graph.get(edge1).add(edge2);
        graph.get(edge2).add(edge1);
    }

    public static class Pair implements Comparable<Pair> {
        int first;
        int second;

        public Pair(int first, int second) {
            this.first = first;
            this.second = second;
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

        public int compareTo(Pair o) {
            // TODO Auto-generated method stub
            if (this.first != o.first)
                return (int) (this.first - o.first);
            else return (int) (this.second - o.second);
        }
    }

    public static class PairC<X, Y> implements Comparable<PairC> {
        X first;
        Y second;

        public PairC(X first, Y second) {
            this.first = first;
            this.second = second;
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

        public int compareTo(PairC o) {
            // TODO Auto-generated method stub
            return o.compareTo((PairC) first);
        }
    }

    static boolean isCollectionsSorted(List<Long> list) {
        if (list.size() == 0 || list.size() == 1) return true;
        for (int i = 1; i < list.size(); i++) if (list.get(i) <= list.get(i - 1)) return false;
        return true;
    }

    static boolean isCollectionsSortedReverseOrder(List<Long> list) {
        if (list.size() == 0 || list.size() == 1) return true;
        for (int i = 1; i < list.size(); i++) if (list.get(i) >= list.get(i - 1)) return false;
        return true;
    }

}