At the school where Vasya is studying, preparations are underway for the graduation ceremony. One of the planned performances is a ball, which will be attended by pairs of boys and girls.

Each class must present two couples to the ball. In Vasya's class, a boys and b girls wish to participate. But not all boys and not all girls are ready to dance in pairs.

Formally, you know k possible one-boy-one-girl pairs. You need to choose two of these pairs so that no person is in more than one pair.

For example, if a=3, b=4, k=4 and the couples (1, 2), (1, 3), (2, 2), (3, 4) are ready to dance together (in each pair, the boy's number comes first, then the girl's number), then the following combinations of two pairs are possible (not all possible options are listed below): 

  * (1, 3) and (2, 2); 
  * (3, 4) and (1, 3); 



But the following combinations are not possible: 

  * (1, 3) and (1, 2) — the first boy enters two pairs; 
  * (1, 2) and (2, 2) — the second girl enters two pairs; 



Find the number of ways to select two pairs that match the condition above. Two ways are considered different if they consist of different pairs.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The first line of each test case contains three integers a, b and k (1 ≤ a, b, k ≤ 2 ⋅ 10^5) — the number of boys and girls in the class and the number of couples ready to dance together.

The second line of each test case contains k integers a_1, a_2, … a_k. (1 ≤ a_i ≤ a), where a_i is the number of the boy in the pair with the number i.

The third line of each test case contains k integers b_1, b_2, … b_k. (1 ≤ b_i ≤ b), where b_i is the number of the girl in the pair with the number i.

It is guaranteed that the sums of a, b, and k over all test cases do not exceed 2 ⋅ 10^5.

It is guaranteed that each pair is specified at most once in one test case.

Output

For each test case, on a separate line print one integer — the number of ways to choose two pairs that match the condition above.

Example

Input


3
3 4 4
1 1 2 3
2 3 2 4
1 1 1
1
1
2 2 4
1 1 2 2
1 2 1 2


Output


4
0
2

Note

In the first test case, the following combinations of pairs fit: 

  * (1, 2) and (3, 4); 
  * (1, 3) and (2, 2); 
  * (1, 3) and (3, 4); 
  * (2, 2) and (3, 4). 



There is only one pair in the second test case.

In the third test case, the following combinations of pairs fit: 

  * (1, 1) and (2, 2); 
  * (1, 2) and (2, 1). 
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 m=i();
    		int k=i();
    		int a[]=ari(k);
    		int b[]=ari(k);
    		int fa[]=new int[n+1];
    		int fb[]=new int[m+1];
    		for(int x=0;x<k;x++)
    		{
    			fa[a[x]]++;
    			fb[b[x]]++;
    		}
    		long c=0l;
    		for(int x=0;x<k;x++)
    		{
    			int va=k-fa[a[x]];
    			int vb=va-(fb[b[x]]-1);
    			c+=vb;
    			//pl(va+" "+vb);
    		}
    		sl(c/2);
    	}
    	p(sb);
    }
    
    static int[] so(int ar[])
    {
    	Integer r[]=new Integer[ar.length];
    	for(int x=0;x<ar.length;x++)r[x]=ar[x];
    	Arrays.sort(r);
    	for(int x=0;x<ar.length;x++)ar[x]=r[x];
    	return ar;
    }
    static long[] so(long ar[])
    {
    	Long r[]=new Long[ar.length];
    	for(int x=0;x<ar.length;x++)r[x]=ar[x];
    	Arrays.sort(r);
    	for(int x=0;x<ar.length;x++)ar[x]=r[x];
    	return ar;
    }
    static char[] so(char ar[])
    {
    	Character r[]=new Character[ar.length];
    	for(int x=0;x<ar.length;x++)r[x]=ar[x];
    	Arrays.sort(r);
    	for(int x=0;x<ar.length;x++)ar[x]=r[x];
    	return ar;
    }
    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 m=a[0];for(int e:a)m=(m>=e)?m:e;return m;}
    static int min(int ...a){int m=a[0];for(int e:a)m=(m<=e)?m:e;return m;}
    static int abs(int a){return Math.abs(a);}
    static long max(long ...a){long m=a[0];for(long e:a)m=(m>=e)?m:e;return m;}
    static long min(long ...a){long m=a[0];for(long e:a)m=(m<=e)?m:e;return m;}
    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 long gcd(long a,long b){return b==0l?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[] si(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])
        	{
        		int vv=(x<<1);
        		for(int y=x*x;y<=n;y+=vv)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(long a[])
    {
    	for(long 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);
    }
}