This is the easy version of this problem. The only difference between easy and hard versions is the constraints on k and m (in this version k=2 and m=3). Also, in this version of the problem, you DON'T NEED to output the answer by modulo.

You are given a sequence a of length n consisting of integers from 1 to n. The sequence may contain duplicates (i.e. some elements can be equal).

Find the number of tuples of m = 3 elements such that the maximum number in the tuple differs from the minimum by no more than k = 2. Formally, you need to find the number of triples of indices i < j < z such that

$$$max(a_i, a_j, a_z) - min(a_i, a_j, a_z) ≤ 2.$$$

For example, if n=4 and a=[1,2,4,3], then there are two such triples (i=1, j=2, z=4 and i=2, j=3, z=4). If n=4 and a=[1,1,1,1], then all four possible triples are suitable.

Input

The first line contains a single integer t (1 ≤ t ≤ 2 ⋅ 10^5) — the number of test cases. Then t test cases follow.

The first line of each test case contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the sequence a.

The next line contains n integers a_1, a_2,…, a_n (1 ≤ a_i ≤ n) — the sequence a.

It is guaranteed that the sum of n for all test cases does not exceed 2 ⋅ 10^5.

Output

Output t answers to the given test cases. Each answer is the required number of triples of elements, such that the maximum value in the triple differs from the minimum by no more than 2. Note that in difference to the hard version of the problem, you don't need to output the answer by modulo. You must output the exact value of the answer.

Example

Input


4
4
1 2 4 3
4
1 1 1 1
1
1
10
5 6 1 3 2 9 8 1 2 4


Output


2
4
0
15
import java.io.*;import java.util.*;import java.math.*;
public class Main
{
	static long mod=1000000007l;
    static int max=Integer.MAX_VALUE,min=Integer.MIN_VALUE;
    static long maxl=Long.MAX_VALUE,minl=Long.MIN_VALUE;
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;
    static StringBuilder sb;
    
    static public void main(String[] args)throws Exception
    {
    	st=new StringTokenizer(br.readLine());
    	int t=i();
    	sb=new StringBuilder(1000000);
    	o:
    	while(t-->0)
    	{
    		int n=i();
    		int ar[]=ari(n);
    		int f[]=new int[n+1];
    		for(int x:ar)f[x]++;
    		long c=0l;
    		for(int x=1;x<=n;x++)
    		{
    			long v=1l*f[x];
    			if(v>=3l)c+=(v*(v-1)*(v-2))/6;
    		}
    		for(int x=1;x<=n;x++)
    		{
    			long a=1l*f[x];
    			long b=1l*f[x-1];
    			if(a>0l&&b>0l)
    			{
    				c+=(((a*(a-1))/2)*b);
    				c+=(((b*(b-1))/2)*a);
    			}
    		}
    		for(int x=2;x<=n;x++)
    		{
    			long a=1l*f[x];
    			long b=1l*f[x-1];
    			long d=1l*f[x-2];
    			if(a>0l&&b>0l&&d>0l)c+=(a*b*d);
    			if(a>0l&&d>0l)
    			{
    				c+=(((a*(a-1))/2)*d);
    				c+=(((d*(d-1))/2)*a);
    			}
    		}
    		sl(c);
    	}
    	p(sb);
    }
    
    static void s(String s){sb.append(s);}
    static void s(int s){sb.append(s);}
    static void s(long s){sb.append(s);}
    static void s(char s){sb.append(s);}
    static void s(double s){sb.append(s);}
    static void ss(){sb.append(' ');}
    static void sl(String s){sb.append(s);sb.append("\n");}
    static void sl(int s){sb.append(s);sb.append("\n");}
    static void sl(long s){sb.append(s);sb.append("\n");}
    static void sl(char s){sb.append(s);sb.append("\n");}
    static void sl(double s){sb.append(s);sb.append("\n");}
    static void sl(){sb.append("\n");}
    static int max(int a,int b){return a>b?a:b;}
    static int min(int a,int b){return a<b?a:b;}
    static int abs(int a){return Math.abs(a);}
    static long max(long a,long b){return a>b?a:b;}
    static long min(long a,long b){return a<b?a:b;}
    static long abs(long a){return Math.abs(a);}
    static int sq(int a){return (int)Math.sqrt(a);}
    static long sq(long a){return (long)Math.sqrt(a);}
    static int gcd(int a,int b){return b==0?a:gcd(b,a%b);}
    static boolean pa(String s,int i,int j)
    {
    	while(i<j)if(s.charAt(i++)!=s.charAt(j--))return false;
    	return true;
    }
    static int ncr(int n,int c,long m)
    {
        long a=1l;
        for(int x=n-c+1;x<=n;x++)a=((a*x)%m);
        long b=1l;
        for(int x=2;x<=c;x++)b=((b*x)%m);
        return (int)((a*(mul((int)b,m-2,m)%m))%m);
    }
    static boolean[] sieve(int n)
    {
        boolean bo[]=new boolean[n+1];
        bo[0]=true;bo[1]=true;
        for(int x=4;x<=n;x+=2)bo[x]=true;
        for(int x=3;x*x<=n;x+=2)if(!bo[x])for(int y=x*x;y<=n;y+=x)bo[y]=true;
        return bo;
    }
    static int[] fac(int n)
    {
        int bo[]=new int[n+1];
        for(int x=1;x<=n;x++)for(int y=x;y<=n;y+=x)bo[y]++;
        return bo;
    }
    static long mul(long a,long b,long m) 
    {
        long r=1l;
        a%=m;  
        while(b>0)
        {
            if((b&1)==1)r=(r*a)%m; 
            b>>=1;
            a=(a*a)%m;  
        } 
        return r; 
    }
    static int i()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }
    static long l()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Long.parseLong(st.nextToken());
    }
    static String s()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return st.nextToken();
    }
    static double d()throws IOException
    {
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        return Double.parseDouble(st.nextToken());
    }
    static void p(Object p){System.out.print(p);}
    static void p(String p){System.out.print(p);}
    static void p(int p){System.out.print(p);}
    static void p(double p){System.out.print(p);}
    static void p(long p){System.out.print(p);}
    static void p(char p){System.out.print(p);}
    static void p(boolean p){System.out.print(p);}
    static void pl(Object p){System.out.println(p);}
    static void pl(String p){System.out.println(p);}
    static void pl(int p){System.out.println(p);}
    static void pl(char p){System.out.println(p);}
    static void pl(double p){System.out.println(p);}
    static void pl(long p){System.out.println(p);}
    static void pl(boolean p){System.out.println(p);}
    static void pl(){System.out.println();}
    static void s(int a[])
    {
    	for(int e:a)
    	{
    		sb.append(e);
    		sb.append(' ');
    	}
    	sb.append("\n");
    }
    static void s(int ar[][])
    {
    	for(int a[]:ar)
    	{
	    	for(int e:a)
	    	{
	    		sb.append(e);
	    		sb.append(' ');
	    	}
	    	sb.append("\n");
    	}
    }
    static void s(char a[])
    {
    	for(char e:a)
    	{
    		sb.append(e);
    		sb.append(' ');
    	}
    	sb.append("\n");
    }
    static void s(char ar[][])
    {
    	for(char a[]:ar)
    	{
	    	for(char e:a)
	    	{
	    		sb.append(e);
	    		sb.append(' ');
	    	}
	    	sb.append("\n");
    	}
    }
    static int[] ari(int n)throws IOException
    {
        int ar[]=new int[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=Integer.parseInt(st.nextToken());
        return ar;
    }
    static int[][] ari(int n,int m)throws IOException
    {
        int ar[][]=new int[n][m];
        for(int x=0;x<n;x++)
        {
        	if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Integer.parseInt(st.nextToken());
        }
        return ar;
    }
    static long[] arl(int n)throws IOException
    {
        long ar[]=new long[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++) ar[x]=Long.parseLong(st.nextToken());
        return ar;
    }
    static long[][] arl(int n,int m)throws IOException
    {
        long ar[][]=new long[n][m];
        for(int x=0;x<n;x++)
        {
        	if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Long.parseLong(st.nextToken());
        }
        return ar;
    }
    static String[] ars(int n)throws IOException
    {
        String ar[]=new String[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++) ar[x]=st.nextToken();
        return ar;
    }
    static double[] ard(int n)throws IOException
    {
        double ar[]=new double[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=Double.parseDouble(st.nextToken());
        return ar;
    }
    static double[][] ard(int n,int m)throws IOException
    {
        double ar[][]=new double[n][m];
        for(int x=0;x<n;x++)
        {
        	if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
            for(int y=0;y<m;y++)ar[x][y]=Double.parseDouble(st.nextToken());
        }
        return ar;
    }
    static char[] arc(int n)throws IOException
    {
        char ar[]=new char[n];
        if(!st.hasMoreTokens())st=new StringTokenizer(br.readLine());
        for(int x=0;x<n;x++)ar[x]=st.nextToken().charAt(0);
        return ar;
    }
    static char[][] arc(int n,int m)throws IOException
    {
        char ar[][]=new char[n][m];
        for(int x=0;x<n;x++)
        {
            String s=br.readLine();
            for(int y=0;y<m;y++)ar[x][y]=s.charAt(y);
        }
        return ar;
    }
    static void p(int ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(int a:ar)
        {
        	sb.append(a);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(int ar[][])
    {
    	StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(int a[]:ar)
        {
            for(int aa:a)
            {
            	sb.append(aa);
            	sb.append(' ');
            }
            sb.append("\n");
        }
        p(sb);
    }
    static void p(long ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(long a:ar)
        {
        	sb.append(a);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(long ar[][])
    {
    	StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(long a[]:ar)
        {
            for(long aa:a)
            {
            	sb.append(aa);
            	sb.append(' ');
            }
            sb.append("\n");
        }
        p(sb);
    }
    static void p(String ar[])
    {
    	int c=0;
    	for(String s:ar)c+=s.length()+1;
        StringBuilder sb=new StringBuilder(c);
        for(String a:ar)
        {
        	sb.append(a);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(double ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(double a:ar)
        {
        	sb.append(a);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(double ar[][])
    {
    	StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(double a[]:ar)
        {
            for(double aa:a)
            {
            	sb.append(aa);
            	sb.append(' ');
            }
            sb.append("\n");
        }
        p(sb);
    }
    static void p(char ar[])
    {
        StringBuilder sb=new StringBuilder(2*ar.length);
        for(char aa:ar)
        {
        	sb.append(aa);
        	sb.append(' ');
        }
        System.out.println(sb);
    }
    static void p(char ar[][])
    {
        StringBuilder sb=new StringBuilder(2*ar.length*ar[0].length);
        for(char a[]:ar)
        {
            for(char aa:a)
            {
            	sb.append(aa);
            	sb.append(' ');
            }
            sb.append("\n");
        }
        p(sb);
    }
}