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.lang.*;
import java.io.*;
import java.math.BigInteger;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.math.BigInteger;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
public class codeee
{		//public static int mod=1000000007;
	 static class Reader {
		 
	        final private int BUFFER_SIZE = 1 << 16;
	        private DataInputStream din;
	        private byte[] buffer;
	        private int bufferPointer, bytesRead;
	 
	        public Reader()
	        {
	            din = new DataInputStream(System.in);
	            buffer = new byte[BUFFER_SIZE];
	            bufferPointer = bytesRead = 0;
	        }
	 
	        public Reader(String file_name) throws IOException
	        {
	            din = new DataInputStream(
	                new FileInputStream(file_name));
	            buffer = new byte[BUFFER_SIZE];
	            bufferPointer = bytesRead = 0;
	        }
	 
	        public String readLine() throws IOException
	        {
	            byte[] buf = new byte[64]; // line length
	            int cnt = 0, c;
	            while ((c = read()) != -1) {
	                if (c == '\n') {
	                    if (cnt != 0) {
	                        break;
	                    }
	                    else {
	                        continue;
	                    }
	                }
	                buf[cnt++] = (byte)c;
	            }
	            return new String(buf, 0, cnt);
	        }
	 
	        public int nextInt() 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 nextLong() 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 nextDouble() 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 long gcd(long x, long p)
	    {
	        if (x == 0)
	            return p;
	         
	        return gcd(p%x, x);
	    }
	 public static HashMap<Integer, Integer> sortByValue(HashMap<Integer, Integer> hm)
	    {
	        // Create a list from elements of HashMap
	        List<Map.Entry<Integer, Integer> > list =
	               new LinkedList<Map.Entry<Integer, Integer> >(hm.entrySet());
	 
	        // Sort the list
	        Collections.sort(list, new Comparator<Map.Entry<Integer, Integer> >() {
	            public int compare(Map.Entry<Integer, Integer> o1,
	                               Map.Entry<Integer, Integer> o2)
	            {
	                return (o1.getValue()).compareTo(o2.getValue());
	            }
	        });
	         
	        // put data from sorted list to hashmap
	        HashMap<Integer, Integer> temp = new LinkedHashMap<Integer, Integer>();
	        for (Map.Entry<Integer, Integer> aa : list) {
	            temp.put(aa.getKey(), aa.getValue());
	        }
	        return temp;
	    }
	 static int sieve =  1000000 ;


	 static boolean[] prime =  new boolean[sieve + 1] ;

	 public static void sieveOfEratosthenes() 
	     { 
	         // FALSE == prime and 1 // TRUE ==  COMPOSITE
	         
	         // time complexity = 0(NlogLogN)== o(N)
	         
	         // gives prime nos bw 1 to N // size - 1e7(at max)
	         
	         for(int i = 4; i<= sieve ; i++)
	         {
	             prime[i] = true  ; i++ ;
	            
	         }
	         
	         for(int p = 3; p*p <= sieve; p++) 
	         { 
	            if(prime[p] == false) 
	             { 
	                     for(int i = p*p; i <= sieve; i += p) 
	                     prime[i] = true; 
	             } 
	             
	             p++ ;
	         } 
	           
	     } 
	 public static void arrInpInt(int [] arr, int n) throws IOException
	 {
		 Reader reader = new Reader();
		 for(int i=0;i<n;i++)
	   		{
	   			arr[i]=reader.nextInt();	
	   		}
	 }
	 public static void arrInpLong(long [] arr, int n) throws IOException
	 {
		 Reader reader = new Reader();
		 for(int i=0;i<n;i++)
	   		{
	   			arr[i]=reader.nextLong();	
	   		}
	 }
	 public static void printArr(int[] arr)
	 {
		 for(int i=0;i<arr.length;i++)
		 {
			 System.out.print(arr[i]+" ");
		 }
		 System.out.println();
	 }
	 public static int[] decSort(int[] arr)
	 {
		  int[] arr1 = Arrays.stream(arr).boxed().sorted(Collections.reverseOrder()).mapToInt(Integer::intValue).toArray();	
		  return arr1;
	 }
	 
	
	//if present - return the first occurrence of the no
	//not present- return the index of next greater value 
	//if greater than all the values return N(taking high=N-1)
	//if smaller than all the values return 0(taking low =0)
	static int lower_bound(int arr[], int low,int high, int X)
	{

	 if (low > high) {
	     return low;
	 }
	 int mid = low + (high - low) / 2;
	 if (arr[mid] >= X) {
	     return lower_bound(arr, low,
	                        mid - 1, X);
	 }

	 return lower_bound(arr, mid + 1,
	                    high, X);
	}
	//if present - return the index of next greater value
	//not present- return the index of next greater value 
	//if greater than all the values return N(taking high=N-1)
	//if smaller than all the values return 0(taking low =0)\
	
	static int upper_bound(int arr[], int low, int high, int X)
{

if (low > high)
    return low;

int mid = low + (high - low) / 2;
if (arr[mid] <= X) {
    return upper_bound(arr, mid + 1,
                       high, X);
}

return upper_bound(arr, low,
                   mid - 1, X);
}
	
	
	 public static class Pair  {// comparator with class
		    int x;
		    int y;
		 public Pair(int x, int y)
		    {
		        this.x = x;
		        this.y = y;
		    }
		}
	
	 public static void sortbyColumn(int arr[][], int col)  // send 2d array and col no
	    {
	        Arrays.sort(arr, new Comparator<int[]>() {       
	          @Override              
	          public int compare(final int[] entry1, 
	                             final int[] entry2) {
	            if (entry1[col] > entry2[col])
	                return 1;
	            else if (entry1[col] < entry2[col])
	                return -1;
	              else return 0;
	          }
	        });
	    }
	 public static void sortbyColumn1(int arr[][], int col)  // send 2d array and col no
	    {
	        Arrays.sort(arr, new Comparator<int[]>() {       
	          @Override              
	          public int compare(final int[] entry1, 
	                             final int[] entry2) {
	            if (entry1[col] > entry2[col])
	                return 1;
	            else if (entry1[col] < entry2[col])
	                return -1;
	            else if(entry1[col] == entry2[col])
	            {
	            	if(entry1[col-1]>entry2[col-1])
	            		return -1;
	            	else if(entry1[col-1]<entry2[col-1])
	            		return 1;
	            	else return 0;
	            }
	              else return 0;
	          }
	        });
	    }
	 public static void print2D(int mat[][])
	    {
	        // Loop through all rows
	        for (int i = 0; i < mat.length; i++)
	 
	        {  // Loop through all elements of current row
	        {
	            for (int j = 0; j < mat[i].length; j++)
	                System.out.print(mat[i][j] + " ");
	        }
	            System.out.println();
	        }
	    }
	     
	    public static class  p
	     {
	    	 int no;
	    	 int h;
	    	 public p(int no, long h)
	    	 {
	    		 this.no=no;
	    		 this.h=(int) h;
	    	 }
	     }
	    
	  static    class com implements Comparator<p>{
	            public int compare(p s1, p s2) {
	                if (s1.h > s2.h)
	                    return -1;
	                else if (s1.h < s2.h)
	                    return 1;
	                else if(s1.h==s2.h)
	                {
	                	if(s1.no>s2.no)return -1;
	                	else return 1;
	                }
	                                return 0;
	                }
	        }
	  

	 
 	public static void main(String args[]) throws NumberFormatException, IOException ,java.lang.Exception
	{
		
		Reader reader = new Reader();
		
		
		//sieveOfEratosthenes();
		//System.out.println(prime[0]+" "+prime[1]+" "+prime[2]+" "+prime[3]+" "+prime[4]);
		//Scanner reader=new Scanner(System.in);
		
		//BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		//int cases=Integer.parseInt(br.readLine());
		//int cases=1;
		int cases=reader.nextInt();
		
   	while (cases-->0){
   		int N=reader.nextInt();
   		//int K=reader.nextInt();
   		//BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));
  // 		int P=reader.nextInt();
   		//int[][] arr=new int[N][N];
   //	int K=reader.nextInt();
   		//int X=reader.nextInt();
   		//int K=reader.nextInt();
   		//int S=reader.nextInt();
   		//int circum=reader.nextInt();
   		//int K=reader.nextInt();
   		//String[] first=br.readLine().split(" ");
   		//int N=Integer.parseInt(first[0]);
   		//char p=first[1].charAt(0);
//   		int P=Integer.parseInt(first[1]);
//   		int K=Integer.parseInt(first[2]);
   		//String[] first=br.readLine().split(" ");
   		//int N=Integer.parseInt(first[0]);
   		//int K=Integer.parseInt(first[1]);
   		//int X=reader.nextInt();
   		//int Y=reader.nextInt();
   		//String s2=br.readLine();
   		//String s3=br.readLine();
   		//char[]  s11=s2.toCharArray();
   		//String[] first1=br.readLine().split(" ");
   		//int C=Integer.parseInt(first1[0]);
   		//int C1=Integer.parseInt(first1[1]);
   		//char[]  s12=s3.toCharArray();
    	//int max=Integer.MIN_VALUE;
   		//int min=Integer.MAX_VALUE;
   		//int ind=-1;
   		//HashMap<Integer,Integer> a1=new HashMap<Integer,Integer>();
   		//HashMap<Long,Long> b1=new HashMap<Long,Long>();
   		HashMap<Integer,Integer> boy=new HashMap<Integer,Integer>();
   		//HashMap<Integer,Integer> map=new HashMap<Integer,Integer>();
   		//TreeSet<Integer> tree =new TreeSet<Integer>(); 
   		//TreeSet<Long> a =new TreeSet<Long>();
   		//TreeSet<Long> b =new TreeSet<Long>();
   		//TreeSet<Integer> map=new TreeSet<Integer>();
   		int[] arr=new int[N];
   		//boolean[]arr1=new boolean[N];
   		//int[] arr2=new int[N];
   		//ArrayList<Integer> no=new ArrayList<Integer>();
   		//ArrayList<Long> sum=new ArrayList<Long>();
   		//int [][] arr=new int[N][5];
        //System.out.println(map);
   		//PriorityQueue<p> Q=new PriorityQueue<p>(new com());
   		//PriorityQueue<Long> w=new PriorityQueue<Long>();
   		
   		//int min=Integer.MAX_VALUE;
   		
   		//System.out.println("max="+max);
   		
   		//ArrayList<ArrayList<Integer>> arr=new ArrayList<ArrayList<Ineteger>>();
   		
   	//	System.out.println(p);
   		long sum=0;
   		for(int i=0;i<N;i++)
   		{
   			arr[i]=reader.nextInt();
   			sum=sum+arr[i];
   			if(boy.containsKey(arr[i]))
   			{
   				boy.replace(arr[i],boy.get(arr[i])+1);
   			}
   			else
   			{
   				boy.put(arr[i], 1);
   			}
   			
   		}
   		if(sum%N!=0)
   		{
   			System.out.println(0);
   		}
   		else
   		{
   			Arrays.sort(arr);
   			long count=0;
   			int need=(int) (((long)sum/(long)N)*2);
   			for(int i=0;i<N;i++)
   			{
   				int rem=need-arr[i];
   				boy.replace(arr[i], boy.get(arr[i])-1);
   				if(rem>=0)
   				{
   					if(boy.containsKey(rem))
   					{
   						count=count+boy.get(rem);
   					}
   				}
   			}
   			System.out.println(count);
   		}
   		
   		}
        //System.out.println(Arrays.toString(sum));    
   		
   	}}