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 class Main {
	static InputReader in = new InputReader(System.in);
	static OutputWriter out = new OutputWriter(System.out);

	public static void main(String[] args) throws IOException {
		int t = i();
		int c = 1;
		sb = new StringBuilder();
		while (t-- > 0) {
//			sb.append("Case #" + c + ": ");
			solve();
			c++;
		}
		out.println(sb.toString());
		out.close();

	}

	static int mod = 1000000007;
	static StringBuilder sb;

	private static void solve() {
		long nn = l();
		long[] arr = readArray(nn * 1L);
		int n = (int) (nn);
		HashMap<Long, Integer> map = new HashMap<>();
		long sum = 0L;
		for (int i = 0; i < n; i++) {
			sum += arr[i];
			map.put(arr[i], map.getOrDefault(arr[i], 0) + 1);
		}

		long res = 0L;
		long us = sum * 2;
		for (int i = 0; i < n; i++) {
			long l = arr[i];
			if (!map.containsKey(l)) {
				continue;
			}
			long rv = (us - n * l) / n;
			if (rv == l) {
				int c = map.get(l);
				res += c * (c - 1L) / 2;
			} else if (map.containsKey(rv)) {
				int c1 = map.get(l);
				int c2 = map.get(rv);
				res += c1 * c2 * 1L;
			}
			map.remove(l);
		}
		sb.append(res);
		sb.append("\n");
	}

	// Fenwick Tree
	static class fenwickTree {
		int n;
		long[] farr;

		fenwickTree(int n, long[] a) {
			this.n = n;
			farr = new long[n + 1];
			for (int i = 0; i < n; i++) {
				update(i + 1, a[i]);
			}
		}

		void update(int i, long val) {
			while (i < farr.length) {
				farr[i] += val;
				i += (i & -i);
			}
		}

		long sum(int i) {
			long sum = 0L;
			while (i > 0) {
				sum += farr[i];
				i -= (i & -i);
			}
			return sum;
		}
	}

// ****CLASS PAIR ************************************************
//	static class Pair implements Comparable<Pair> {
//		int sp;
//		int ep;
//
//		Pair(int sp, int ep) {
//			this.sp = sp;
//			this.ep = ep;
//		}
//
//		public int compareTo(Pair o) {
//			return this.sp - o.sp;
//		}
//
//	}

	static class Pair implements Comparable<Pair> {
		char ch;
		ArrayList<Integer> idxs;

		Pair(char ch, ArrayList<Integer> idxs) {
			this.ch = ch;
			this.idxs = idxs;
		}

		public int compareTo(Pair o) {
			return o.idxs.size() - this.idxs.size();
		}

	}

	static class Edge implements Comparable<Edge> {
		int u;
		int v;
		int wt;

		Edge(int u, int v, int wt) {
			this.u = u;
			this.v = v;
			this.wt = wt;
		}

		public int compareTo(Edge o) {
			return this.wt - o.wt;
		}
	}

// *************Disjoint Set Union*********//
	static class dsu {
		int[] par;
		int[] rank;

		dsu(int n) {
			par = new int[n + 1];
			rank = new int[n + 1];
			for (int i = 0; i <= n; i++) {
				par[i] = i;
				rank[i] = 1;
			}
		}

		int find(int a) {
			if (par[a] == a) {
				return a;
			}
			int x = find(par[a]);
			par[a] = x;
			return x;
		}

		boolean union(int a, int b) {
			int pa = find(a);
			int pb = find(b);
			if (pa == pb) {
				return false;
			}
			if (rank[pa] > rank[pb]) {
				par[pb] = pa;
			} else if (rank[pb] > rank[pa]) {
				par[pa] = pb;
			} else {
				par[pa] = pb;
				rank[pb]++;
			}
			return true;
		}

	}

	// **************NCR%P******************
	static long ncr(int n, int r) {
		if (r > n)
			return (long) 0;
		long[] fact = new long[(int) 1e6 + 10];
		fact[0] = fact[1] = 1;
		for (int i = 2; i < fact.length; i++) {
			fact[i] = ((long) (i % mod) * (long) (fact[i - 1] % mod)) % mod;
		}
		long res = fact[n] % mod;
		res = ((long) (res % mod) * (long) (p(fact[r], mod - 2) % mod)) % mod;
		res = ((long) (res % mod) * (long) (p(fact[n - r], mod - 2) % mod)) % mod;
		return res;
	}

	static ArrayList<Integer> divisors(int n) {
		ArrayList<Integer> al = new ArrayList<>();
		for (int i = 1; i * i <= n; i++) {
			if (n % i == 0) {
				if (n == i * i) {
					al.add(i);
				} else {
					al.add(i);
					al.add(n / i);
				}
			}
		}
		Collections.sort(al);
		return al;
	}

	static long p(long x, long y)// POWER FXN //
	{
		if (y == 0)
			return 1;

		long res = 1;
		while (y > 0) {
			if (y % 2 == 1) {
				res = (res * x) % mod;
				y--;
			}

			x = (x * x) % mod;
			y = y / 2;

		}
		return res % mod;
	}

	private static boolean pow2(int i) {
		return (i & (i - 1)) == 0;
	}

	private static void sort(int[] arr) {
		int n = arr.length;
		ArrayList<Integer> res = new ArrayList<>();
		for (int a : arr) {
			res.add(a);
		}
		Collections.sort(res);
		for (int i = 0; i < n; i++) {
			arr[i] = res.get(i);
		}
	}

	private static void sort(long[] arr) {
		int n = arr.length;
		ArrayList<Long> res = new ArrayList<>();
		for (long a : arr) {
			res.add(a);
		}
		Collections.sort(res);
		for (int i = 0; i < n; i++) {
			arr[i] = res.get(i);
		}
	}

	private static void revSort(int[] arr) {
		int n = arr.length;
		ArrayList<Integer> res = new ArrayList<>();
		for (int a : arr) {
			res.add(a);
		}
		Collections.sort(res, Collections.reverseOrder());
		for (int i = 0; i < n; i++) {
			arr[i] = res.get(i);
		}
	}

	private static ArrayList<Integer> sieveOfEratosthenes(int n) {
		boolean[] arr = new boolean[n + 1];

		arr[0] = arr[1] = true;
		for (int i = 2; i * i <= n; i++) {
			if (!arr[i]) {
				for (int j = i * i; j <= n; j += i) {
					arr[j] = true;
				}
			}
		}
		ArrayList<Integer> primes = new ArrayList<>();
		for (int i = 2; i <= n; i++) {
			if (!arr[i]) {
				primes.add(i);
			}
		}
		return primes;
	}

	private static ArrayList<Integer> segmentedSieve(int s, int e) {
		int len = (int) (Math.sqrt(e) + 1);
		ArrayList<Integer> primes = sieveOfEratosthenes(len);
		boolean[] arr2 = new boolean[e - s + 1];
		if (s == 1) {
			arr2[0] = true;
		}
		ArrayList<Integer> res = new ArrayList<>();
		for (int p : primes) {

			int st = (int) (p * (Math.ceil((double) s / p)));
			if (st < s) {
				st += p;
			}
			if (st == p) {
				st += p;
			}
			for (int i = st; i <= e; i += p) {
				arr2[i - s] = true;
			}
		}
		for (int i = 0; i < arr2.length; i++) {
			if (!arr2[i]) {
				res.add(i + s);
			}
		}
		return res;
	}

	private static long pow(int n, int k) {
		long res = 1;
		long num = (long) n;
		while (k > 0) {
			if ((k & 1) == 1) {
				res = (res * num) % mod;
			}
			k /= 2;
			num = num * num % mod;
		}
		return res;
	}

	private static int countDigits(int n) {
		int c = 0;
		while (n != 0) {
			c++;
			n /= 10;
		}
		return c;
	}

	private static boolean palindrome(String str) {
		int s = 0;
		int e = str.length() - 1;
		while (s < e) {
			if (str.charAt(s) != str.charAt(e)) {
				return false;
			}
			s++;
			e--;
		}
		return true;
	}

	private static void reverse(int[] arr, int s, int e) {
		while (s < e) {
			int temp = arr[s];
			arr[s++] = arr[e];
			arr[e--] = temp;
		}
	}

	private static int getMax(int[] arr, int s, int e) {
		int maxi = s;
		for (int i = s + 1; i <= e; i++) {
			if (arr[i] > arr[maxi]) {
				maxi = i;
			}
		}
		return maxi;
	}

	private static int getMin(int[] arr, int s, int e) {
		int mini = s;
		for (int i = s + 1; i <= e; i++) {
			if (arr[i] < arr[mini]) {
				mini = i;
			}
		}
		return mini;
	}

	// ******LOWEST COMMON MULTIPLE************************
	private static long lcm(long n1, long n2) {
		return (n1 * n2) / gcd(n1, n2);
	}

	private static int lcm(int n1, int n2) {
		return (n1 * n2) / gcd(n1, n2);
	}

	// ***********GCD*****************
	private static long gcd(long num1, long num2) {
		if (num2 == 0) {
			return num1;
		}
		return gcd(num2, num1 % num2);
	}

	private static int gcd(int num1, int num2) {
		if (num2 == 0) {
			return num1;
		}
		return gcd(num2, num1 % num2);
	}

	// **************PRIME FACTORIZE **********************************//
	static TreeMap<Long, Long> prime(long n) {
		TreeMap<Long, Long> h = new TreeMap<>();
		long num = n;
		for (int i = 2; i <= Math.sqrt(num); i++) {
			if (n % i == 0) {
				long nt = 0L;
				while (n % i == 0) {
					n = n / i;
					nt++;
				}
				h.put(i * 1L, nt);
			}
		}
		if (n != 1)
			h.put(n, 1L);
		return h;

	}

	static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int Int() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public String String() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public String next() {
			return String();
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}

	static class OutputWriter {
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}

		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		public void println(Object... objects) {
			print(objects);
			writer.println();
		}

		public void close() {
			writer.close();
		}

		public void flush() {
			writer.flush();
		}
	}

//*****************INPUT PATTERN******************************************
	public static int i() {
		return in.Int();
	}

	public static long l() {
		String s = in.String();
		return Long.parseLong(s);
	}

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

	public static int[] readArray(int n) {
		int A[] = new int[n];
		for (int i = 0; i < n; i++) {
			A[i] = i();
		}
		return A;
	}

	public static long[] readArray(long n) {
		long A[] = new long[(int) n];
		for (int i = 0; i < n; i++) {
			A[i] = l();
		}
		return A;
	}

}
