It is the hard version of the problem. The only difference is that in this version 1 ≤ n ≤ 300.

In the cinema seats can be represented as the table with n rows and m columns. The rows are numbered with integers from 1 to n. The seats in each row are numbered with consecutive integers from left to right: in the k-th row from m (k - 1) + 1 to m k for all rows 1 ≤ k ≤ n.

1| 2| ⋅⋅⋅| m - 1| m  
---|---|---|---|---  
m + 1| m + 2| ⋅⋅⋅| 2 m - 1| 2 m  
2m + 1| 2m + 2| ⋅⋅⋅| 3 m - 1| 3 m  
\vdots| \vdots| \ddots| \vdots| \vdots  
m (n - 1) + 1| m (n - 1) + 2| ⋅⋅⋅| n m - 1| n m  
The table with seats indices

There are nm people who want to go to the cinema to watch a new film. They are numbered with integers from 1 to nm. You should give exactly one seat to each person.

It is known, that in this cinema as lower seat index you have as better you can see everything happening on the screen. i-th person has the level of sight a_i. Let's define s_i as the seat index, that will be given to i-th person. You want to give better places for people with lower sight levels, so for any two people i, j such that a_i < a_j it should be satisfied that s_i < s_j.

After you will give seats to all people they will start coming to their seats. In the order from 1 to nm, each person will enter the hall and sit in their seat. To get to their place, the person will go to their seat's row and start moving from the first seat in this row to theirs from left to right. While moving some places will be free, some will be occupied with people already seated. The inconvenience of the person is equal to the number of occupied seats he or she will go through.

Let's consider an example: m = 5, the person has the seat 4 in the first row, the seats 1, 3, 5 in the first row are already occupied, the seats 2 and 4 are free. The inconvenience of this person will be 2, because he will go through occupied seats 1 and 3.

Find the minimal total inconvenience (the sum of inconveniences of all people), that is possible to have by giving places for all people (all conditions should be satisfied).

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. Description of the test cases follows.

The first line of each test case contains two integers n and m (1 ≤ n, m ≤ 300) — the number of rows and places in each row respectively.

The second line of each test case contains n ⋅ m integers a_1, a_2, …, a_{n ⋅ m} (1 ≤ a_i ≤ 10^9), where a_i is the sight level of i-th person.

It's guaranteed that the sum of n ⋅ m over all test cases does not exceed 10^5.

Output

For each test case print a single integer — the minimal total inconvenience that can be achieved.

Example

Input


7
1 2
1 2
3 2
1 1 2 2 3 3
3 3
3 4 4 1 1 1 1 1 2
2 2
1 1 2 1
4 2
50 50 50 50 3 50 50 50
4 2
6 6 6 6 2 2 9 6
2 9
1 3 3 3 3 3 1 1 3 1 3 1 1 3 3 1 1 3


Output


1
0
4
0
0
0
1

Note

In the first test case, there is a single way to give seats: the first person sits in the first place and the second person — in the second. The total inconvenience is 1.

In the second test case the optimal seating looks like this: 

<image>

In the third test case the optimal seating looks like this: 

<image>

The number in a cell is the person's index that sits on this place.
import java.util.*;
import java.io.*;
// import java.lang.*;
// import java.math.*;

public class Codeforces {
    static FastReader sc=new FastReader();
	static PrintWriter out=new PrintWriter(System.out);
	static long mod=1000000007;
	// static long mod=998244353;
	static int MAX=Integer.MAX_VALUE;
	static int MIN=Integer.MIN_VALUE;
	static long MAXL=Long.MAX_VALUE;
	static long MINL=Long.MIN_VALUE;
	static ArrayList<Integer> graph[];
	static long fact[]; 
	public static void main (String[] args) throws java.lang.Exception
	{
		// code goes here
		int t=I();
		while(t-->0)
		{
			// int n=I(),m=I();
			// int a[]=new int[n*m];
			// int b[]=new int[n*m];
			// HashMap<Integer,Integer> in=new HashMap<>();
			// HashMap<Integer,ArrayList<Integer>> hm1=new HashMap<>();
			// for(int i=0;i<n*m;i++){
			// 	a[i]=I();
			// 	b[i]=a[i];
			// }
			// sort(b);
			// int c=n*m;
			// for(int i=n*m-1;i>=0;i--){
			// 	if(hm1.containsKey(b[i])){
			// 		ArrayList<Integer> arr=hm1.get(b[i]);
			// 		arr.add(c);
			// 		hm1.put(b[i],arr);
			// 	}else{
			// 		ArrayList<Integer> arr=new ArrayList<>();
			// 		arr.add(c);
			// 		hm1.put(b[i],arr);
			// 	}
			// 	c--;
			// }
			// // for(Map.Entry<Integer,ArrayList<Integer>> e:hm1.entrySet()){
			// // 	Collections.reverse(e.getValue());
			// // }
			// // for(Map.Entry<Integer,ArrayList<Integer>> e:hm1.entrySet()){
			// // 	out.print(e.getKey()+"->");
			// // 	out.println(e.getValue());
			// // }
			// long ans=0;
			// FenwickTree ft=new FenwickTree(n*m);
			// for(int i=0;i<n*m;i++){
			// 	int z=in.getOrDefault(a[i],0);
			// 	in.put(a[i],in.getOrDefault(a[i],0)+1);
			// 	int index=hm1.get(a[i]).get(z);
			// 	ans+=ft.get(index)-ft.get((index-1)/m)*m;
			// 	ft.update(index,1);
			// }
			// out.println(ans);
			int n=I(),m=I();
			int a[]=new int[n*m];
			pair p[]=new pair[n*m];
			for(int i=0;i<n*m;i++){
				a[i]=I();
				p[i]=new pair(a[i],i+1);
			}
			Arrays.sort(p,new myComp());
			// printArray(p);
			long ans=0;
			for(int i=0;i<n;i++){
				int x=i*m,y=(i+1)*m;
				// out.println(x+" "+y);
				for(int j=x;j<y;j++){
					for(int k=x;k<j;k++){
						// if(p[k].a!=p[j].a && p[k].b<p[j].b)ans++;\
						if(p[k].a==p[j].a)continue;
						if(p[k].b<p[j].b)ans++;
					}
				}
			}
			out.println(ans);
		}
		out.close();
	}
	// Fenwick / BinaryIndexed  Tree  USE IT - FenwickTree ft1=new FenwickTree(n);
	public static class FenwickTree
	{
		int farr[];
		int n;
		public FenwickTree(int c)
		{
			n=c+1;
			farr=new int[n];
		}
		// public void update_range(int l,int r,long p)
		// {
		// 	update(l,p);
		// 	update(r+1,(-1)*p);
		// }
		public void update(int x,int p)
		{
			for(;x<n;x+=x&(-x))
			{
				farr[x]+=p;
			}
		}
		public long get(int x)
		{
			long ans=0;
			for(;x>0;x-=x&(-x))
			{
				ans=ans+farr[x];
			}
			return ans;
		}
	}
	public static class pair
    {
    	int a;
    	int b;
    	public pair(int val,int index)
    	{
    	    a=val;
    	    b=index;
    	}
    }
	public static class myComp implements Comparator<pair>
	{
		//sort in ascending order.
		public int compare(pair p1,pair p2)
		{
			if(p1.a==p2.a)
    	    return 0;
    	    else if(p1.a<p2.a)
    	    return -1;
    	    else
    	    return 1;
		}
		//sort in descending order.
		// public int compare(pair p1,pair p2)
    	// {
    	//     if(p1.a==p2.a)
    	//     return 0;
    	//     else if(p1.a<p2.a)
    	//     return 1;
    	//     else
    	//     return -1;
    	// }
	}
	public static long nPr(int n,int r)
	{
		long ans=divide(fact(n),fact(n-r),mod);
		return ans;
	}
	public static long nCr(int n,int r)
	{
		long ans=divide(fact[n],mul(fact[n-r],fact[r]),mod);
		return ans;
	}
	public static long kadane(long a[],int n)
	{
		long max_sum=Long.MIN_VALUE,max_end=0;
		for(int i=0;i<n;i++){
			max_end+=a[i];
			if(max_sum<max_end){max_sum=max_end;}
			if(max_end<0){max_end=0;}
		}
		return max_sum;
	}
	public static void DFS(int s,boolean visited[])
	{
		visited[s]=true;
		for(int i:graph[s]){
			if(!visited[i]){
				DFS(i,visited);
			}
		}
	}
	public static void setGraph(int n,int m)throws IOException
	{
		graph=new ArrayList[n+1];
		for(int i=0;i<=n;i++){
			graph[i]=new ArrayList<>();
		}
		for(int i=0;i<m;i++){
			int u=I(),v=I();
			graph[u].add(v);
			graph[v].add(u);
		}
	}
	public static int BS(long a[],long x,int ii,int jj)
	{
		// int n=a.length;
		int mid=0;
		int i=ii,j=jj;
		while(i<=j)
		{
			mid=(i+j)/2;
			if(a[mid]<x){
				i=mid+1;
			}else if(a[mid]>x){
				j=mid-1;
			}else{
				return mid;
			}
		}
		return -1;
	}
	public static int lower_bound(int arr[],int s, int N, int X)
	{
		if(arr[N]<X)return N;
		if(arr[0]>X)return -1;
		int left=s,right=N;
		while(left<right){
			int mid=(left+right)/2;
			if(arr[mid]==X)
			return mid;
			else if(arr[mid]>X){
				if(mid>0 && arr[mid]>X && arr[mid-1]<=X){
					return mid-1;
				}else{
					right=mid-1;
				}
			}else{
				if(mid<N && arr[mid+1]>X && arr[mid]<=X){
					return mid;
				}else{
					left=mid+1;
				}
			}
		}
		return left;
	}
	public static int computeXOR(int n) //compute XOR of all numbers between 1 to n.
    {
        if (n % 4 == 0)
            return n;
        if (n % 4 == 1)
            return 1;
        if (n % 4 == 2)
            return n + 1;
        return 0;
    }
	public static ArrayList<Integer> primeSieve(int n)
	{
	    ArrayList<Integer> arr=new ArrayList<>();
	    boolean prime[] = new boolean[n + 1];
        for (int i = 0; i <= n; i++)
        prime[i] = true;
        for (int p = 2; p * p <= n; p++)
        {
            if (prime[p] == true)
            {
                for (int i = p * p; i <= n; i += p)
                prime[i] = false;
            }
        }
        for (int i = 2; i <= n; i++)
        {
            if (prime[i] == true)
            arr.add(i);
        }
        return arr;
	}

	

	//Disjoint Set Union
	public static class DSU
	{
	    int par[],rank[];
	    public DSU(int c)
	    {
	        par=new int[c+1];
	        rank=new int[c+1];
	        for(int i=0;i<=c;i++)
	        {
	            par[i]=i;
	            rank[i]=0;
	        }
	    }
	    public int find(int a)
	    {
	        if(a==par[a])
	        return a;
	        return par[a]=find(par[a]);
	    }
	    public void union(int a,int b)
	    {
	        int a_rep=find(a),b_rep=find(b);
	        if(a_rep==b_rep)
	        return;
	        if(rank[a_rep]<rank[b_rep])
	        par[a_rep]=b_rep;
	        else if(rank[a_rep]>rank[b_rep])
	        par[b_rep]=a_rep;
	        else
	        {
	            par[b_rep]=a_rep;
	            rank[a_rep]++;
	        }
	    }
	}
    public static class myComp1 implements Comparator<pair1>
    {
		//sort in ascending order.
    	public int compare(pair1 p1,pair1 p2)
    	{
    	    if(p1.a==p2.a)
    	    return 0;
    	    else if(p1.a<p2.a)
    	    return -1;
    	    else
    	    return 1;
    	}
		//sort in descending order.
		// public int compare(pair p1,pair p2)
    	// {
    	//     if(p1.a==p2.a)
    	//     return 0;
    	//     else if(p1.a<p2.a)
    	//     return 1;
    	//     else
    	//     return -1;
    	// }
    }
	public static class pair1
    {
    	long a;
    	long b;
    	public pair1(long val,long index)
    	{
    	    a=val;
    	    b=index;
    	}
    }
    public static ArrayList<pair1> mergeIntervals(ArrayList<pair1> arr)
	{
	    //****************use this in main function-Collections.sort(arr,new myComp1());
	    ArrayList<pair1> a1=new ArrayList<>();
	    if(arr.size()<=1)
	    return arr;
	    a1.add(arr.get(0));
	    int i=1,j=0;
	    while(i<arr.size())
	    {
	        if(a1.get(j).b<arr.get(i).a)
	        {
	           a1.add(arr.get(i));
	           i++;
	           j++;
	        }
	        else if(a1.get(j).b>arr.get(i).a && a1.get(j).b>=arr.get(i).b)
	        {
	            i++;
	        }
	        else if(a1.get(j).b>=arr.get(i).a)
	        {
	            long a=a1.get(j).a;
	            long b=arr.get(i).b;
	            a1.remove(j);
	            a1.add(new pair1(a,b));
	            i++;
	        }
	    }
	    return a1;
	}
	public static boolean isPalindrome(String s,int n)
	{
		for(int i=0;i<=n/2;i++){
			if(s.charAt(i)!=s.charAt(n-i-1)){
				return false;
			}
		}
		return true;
	}
	public static int gcd(int a,int b)
	{
	    if(b==0)
	    return a;
	    else
	    return gcd(b,a%b);
	}
	public static long gcd(long a,long b)
	{
	    if(b==0)
	    return a;
	    else
	    return gcd(b,a%b);
	}
	public static long fact(long n)
	{
		long fact=1;
		for(long i=2;i<=n;i++){
			fact=((fact%mod)*(i%mod))%mod;
		}
		return fact;
	}
	public static long fact(int n)
	{
		long fact=1;
		for(int i=2;i<=n;i++){
			fact=((fact%mod)*(i%mod))%mod;
		}
		return fact;
	} 
	public static boolean isPrime(int n) 
	{ 
	    if (n <= 1) 
	        return false; 
	    if (n <= 3) 
	        return true; 
	    if (n % 2 == 0 || n % 3 == 0) 
	        return false; 
	    double sq=Math.sqrt(n);
	  
	    for (int i = 5; i <= sq; i = i + 6) 
	        if (n % i == 0 || n % (i + 2) == 0) 
	            return false; 
	    return true; 
	} 
    public static boolean isPrime(long n) 
	{ 
	    if (n <= 1) 
	        return false; 
	    if (n <= 3) 
	        return true; 
	    if (n % 2 == 0 || n % 3 == 0) 
	        return false; 
	    double sq=Math.sqrt(n);
	
	    for (int i = 5; i <= sq; i = i + 6) 
	        if (n % i == 0 || n % (i + 2) == 0) 
	            return false; 
	    return true; 
	}
	public static void printArray(long a[])
	{
		for(int i=0;i<a.length;i++){
			System.out.print(a[i]+" ");
		}
		System.out.println();
	}
	public static void printArray(int a[])
	{
		for(int i=0;i<a.length;i++){
			System.out.print(a[i]+" ");
		}
		System.out.println();
	}
	public static void printArray(char a[])
	{
		for(int i=0;i<a.length;i++){
			System.out.print(a[i]);
		}
		System.out.println();
	}
	public static void printArray(String a[])
	{
		for(int i=0;i<a.length;i++){
			System.out.print(a[i]+" ");
		}
		System.out.println();
	}
	public static void printArray(boolean a[])
	{
		for(int i=0;i<a.length;i++){
			System.out.print(a[i]+" ");
		}
		System.out.println();
	}
	public static void printArray(pair a[])
	{
		for(pair p:a){
			System.out.println(p.a+"->"+p.b);
		}
	}
	public static void printArray(int a[][])
	{
		for(int i=0;i<a.length;i++){
			for(int j=0;j<a[i].length;j++){
				System.out.print(a[i][j]+" ");
			}System.out.println();
		}
	}
	public static void printArray(long a[][])
	{
		for(int i=0;i<a.length;i++){
			for(int j=0;j<a[i].length;j++){
				System.out.print(a[i][j]+" ");
			}System.out.println();
		}
	}
	public static void printArray(char a[][])
	{
		for(int i=0;i<a.length;i++){
			for(int j=0;j<a[i].length;j++){
				System.out.print(a[i][j]+" ");
			}System.out.println();
		}
	}
	public static void printArrayL(ArrayList<Long> arr)
	{
		for(int i=0;i<arr.size();i++){
			System.out.print(arr.get(i)+" ");
		}
		System.out.println();
	}
	public static void printArrayI(ArrayList<Integer> arr)
	{
		for(int i=0;i<arr.size();i++){
			System.out.print(arr.get(i)+" ");
		}
		System.out.println();
	}
	public static void printArrayS(ArrayList<String> arr)
	{
		for(int i=0;i<arr.size();i++){
			System.out.print(arr.get(i)+" ");
		}
		System.out.println();
	}
	public static void printMapInt(HashMap<Integer,Integer> hm){
		for(Map.Entry<Integer,Integer> e:hm.entrySet()){
			System.out.println(e.getKey()+"->"+e.getValue());
		}System.out.println();
	}
	public static void printMapLong(HashMap<Long,Long> hm){
		for(Map.Entry<Long,Long> e:hm.entrySet()){
			System.out.println(e.getKey()+"->"+e.getValue());
		}System.out.println();
	}

	//Modular Arithmetic

	public static long add(long a,long b)
	{
		a+=b;
		if(a>=mod)a-=mod;
		return a;
	}
	public static long sub(long a,long b)
	{
		a-=b;
		if(a<0)a+=mod;
		return a;
	}
	public static long mul(long a,long b)
	{
		return ((a%mod)*(b%mod))%mod;
	}
	public static long divide(long a,long b,long m)
	{
		a=mul(a,modInverse(b,m));
		return a;
	}
	public static long modInverse(long a,long m)
	{
		int x=0,y=0;
		own p=new own(x,y);
		long g=gcdExt(a,m,p);
		if(g!=1){
			out.println("inverse does not exists");
			return -1;
		}else{
			long res=((p.a%m)+m)%m;
			return res;
		}
	}
	public static long gcdExt(long a,long b,own p)
	{
		if(b==0){
			p.a=1;
			p.b=0;
			return a;
		}
		int x1=0,y1=0;
		own p1=new own(x1,y1);
		long gcd=gcdExt(b,a%b,p1);
		p.b=p1.a - (a/b) * p1.b;
		p.a=p1.b;
		return gcd;
	}
	public static long pwr(long m,long n)
	{
		long res=1;
		m=m%mod;
		if(m==0)
		return 0;
		while(n>0)
		{
			if((n&1)!=0)
			{
				res=(res*m)%mod;
			}
			n=n>>1;
			m=(m*m)%mod;
		}
		return res;
	}
	public static class own
    {
    	long a;
    	long b;
    	public own(long val,long index)
    	{
    	    a=val;
    	    b=index;
    	}
    }

	//Modular Airthmetic

	public static void sort(int[] A)
	{
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            int tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
    }
	public static void sort(char[] A)
	{
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            char tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
    }
    public static void sort(long[] A)
	{
	    int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i)
		{
            long tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
	    Arrays.sort(A);
	}
	public static int i(char ch){return Integer.parseInt(String.valueOf(ch));}
	public static int I(){return sc.I();}
    public static long L(){return sc.L();}
    public static String S(){return sc.S();}
    public static double D(){return sc.D();}
}
class FastReader {  
    BufferedReader br;
    StringTokenizer st;
    public FastReader(){
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    String next(){
        while (st == null || !st.hasMoreElements()){
            try {
                st = new StringTokenizer(br.readLine());
            }
            catch (IOException e){
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
    int I(){ 
        return Integer.parseInt(next());
    }
    long L(){ 
        return Long.parseLong(next());
    }
    double D(){
         return Double.parseDouble(next());
    }
    String S(){
        String str = "";
        try 
        {
            str = br.readLine();
        }
        catch (IOException e)
        {
            e.printStackTrace();
        }
        return str;
    }
}
