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.
//package codechef;

import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
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.Map;
import java.util.Set;
import java.util.Stack;
import java.util.TreeMap;






public class cp_2 {
	static int mod=(int)1e9+7;
	
		//static  Reader sc=new Reader();
	   static FastReader sc=new FastReader(System.in);
	 
	
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		//FastReader sc=new FastReader();
			
			
		int t=sc.nextInt();
		while(t-->0)
		{

			int n=sc.nextInt(),m=sc.nextInt();
			int arr[][]=new int[n][m];
			TreeMap<Integer,Integer> map=new TreeMap<Integer, Integer>();
			for(int i=0;i<n;i++)
			for(int j=0;j<m;j++)
			{
			arr[i][j]=sc.nextInt();
			map.put(arr[i][j], map.getOrDefault(arr[i][j], 0)+1);
			}
		
			int pos[][]=new int[n][m];
			int i=0,j=0;
			
			HashMap<Integer,TreeMap<Integer,Stack<Integer>>> lastpos=new HashMap<Integer, TreeMap<Integer,Stack<Integer>>>();
			for(Map.Entry<Integer, Integer> e: map.entrySet())
			{
				int count=e.getValue();
				while(count-->0)
				{
					pos[i][j]=e.getKey();
					j++;
					if(j==m)
					{
						j=0;
						i++;
					}
				}
				lastpos.put(e.getKey(), new TreeMap<Integer, Stack<Integer>>());
			}

			for(i=0;i<n;i++)
			{
					for(j=0;j<m;j++)
					{
							lastpos.get(pos[i][j]).putIfAbsent(i, new Stack<Integer>());
							lastpos.get(pos[i][j]).get(i).push(j);
					}
			}
			// out.println(lastpos);
			long ans=0;
			segment s=new segment(n*m);
			for(i=0;i<n;i++)
			{
				for(j=0;j<m;j++)
				{
					int sight=arr[i][j];
					Map.Entry<Integer, Stack<Integer>> position=lastpos.get(sight).firstEntry();
					int col=position.getValue().pop();
					
					ans+=s.find(position.getKey()*m, position.getKey()*m+col);
					s.doUP(position.getKey()*m+col);
					if(position.getValue().isEmpty())
					lastpos.get(sight).remove(position.getKey());
				}
			}
			out.println(ans);
		}
			
			out.flush();
			out.close();
			System.gc();
	
	}
	
	
	


	/*
	   ...SOLUTION ENDS HERE...........SOLUTION ENDS HERE...
	 */
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	static void swap(int arr[],int i,int j)
	{
		int temp=arr[i];
		arr[i]=arr[j];
		arr[j]=temp;
	}

	
	
	static boolean util(int a,int b,int c)
	{
		if(b>a)util(b, a, c);
		
		while(c>=a)
		{
			c-=a;
			if(c%b==0)
				return true;
		}
		
		
		return (c%b==0);
	}
	
	static boolean check(char arr[][], int i,int j)
	{
		int cnt=0;
		for(int k=i;k<i+2;k++)
		{
			for(int l=j;l<j+2;l++)
			{
				if(arr[k][l]=='#')
					cnt++;
			}
		}
		
		if(cnt!=2)
			return true;
		return false;
		
		
	}
	
	static void flag(boolean flag)
	   {
	       out.println(flag ? "YES" : "NO");
	       out.flush();
	   }
	   
	static ArrayList<Long> luckNums;
	static void luckyNum(long x,long p10)
	{
		luckNums.add(x);
		if(x>(long)1e10)
			return;
		luckyNum(x+4*p10, p10*10);
		luckyNum(x+7*p10, p10*10);
		
	}
	
	 /*                     
	    Map<Long,Long> map=new HashMap<>();
	             for(int i=0;i<n;i++)
	               {
	                  if(!map.containsKey(a[i]))
	                   map.put(a[i],1);
	                 else
	                   map.replace(a[i],map.get(a[i])+1);
	               }
	     
	    Set<Map.Entry<Long,Long>> hmap=map.entrySet();
	             for(Map.Entry<Long,Long> data : hmap)
	               {
	          
	               }
	       
	   Iterator<Integer> it = set.iterator();
	          while(it.hasNext()) 
	           { 
	            int x=it.next();
	           }
	   */

	
	
	
	
	
	static class segment
	{
	public int st[];
	private int n;
	segment(int size)
	{
	n=1<<(int)Math.ceil(Math.log(size)/Math.log(2));
	st=new int[n<<1];
	}
	void doUP(int index)
	{
	update(1, 0, n-1,index);
	}
	int find(int start,int end)
	{
	return query(1, 0, n-1, start, end);
	}
	void update(int v,int vl,int vr,int x)
	{
	if(x<vl || x>vr)
	return;
	if(vl==x && vr==x)
	st[v]=1;
	else
	{
	int mid=(vl+vr)>>1;
	update(v<<1, vl, mid,x);
	update((v<<1)|1, mid+1,vr,x);
	st[v]=st[v<<1]+st[(v<<1)|1];
	}
	}
	int query(int v,int vl,int vr,int l,int r)
	{
	if(vl>r || vr<l)
	return 0;
	if(vl==l && vr==l)
	return st[v];
	else
	{
	int mid=(vl+vr)>>1;
	return query(v<<1, vl, mid, l, Math.min(r, mid))+query((v<<1)|1, mid+1, vr, Math.max(l, mid+1), r);
	}
	}
	void printSegment()
	{
	for(int i=0;i<n;i++)
	out.print(st[i]+" ");
	out.println();
	}
}



	
	
	
	
	
	
	
	static void print(int a[])
	  {
	     int n=a.length;
	     for(int i=0;i<n;i++)
	       {
	          out.print(a[i]+" ");
	       }
	     out.println();
	     out.flush();
	  }
	static void print(long a[])
	  {
	     int n=a.length;
	     for(int i=0;i<n;i++)
	       {
	          out.print(a[i]+" ");
	       }
	     out.println();
	     out.flush();
	  } 
	static void print_int(ArrayList<Integer> al)
	  {
	     int si=al.size();
	     for(int i=0;i<si;i++)
	       {
	          out.print(al.get(i)+" ");
	       }
	     out.println();
	     out.flush();
	  }
	static void print_long(ArrayList<Long> al)
	  {
	     int si=al.size();
	     for(int i=0;i<si;i++)
	       {
	          out.print(al.get(i)+" ");
	       }
	     out.println();
	     out.flush();
	  }
	  
	static int LowerBound(int a[], int x) 
	 { // x is the target value or key
	  int l=-1,r=a.length;
	  while(l+1<r) {
	    int m=(l+r)>>>1;
	    if(a[m]>=x) r=m;
	    else l=m;
	  }
	  return r;
	}
	
	
	static int lowerIndex(int arr[], int n, int x)
    {
        int l = 0, h = n - 1;
        while (l <= h)
        {
            int mid = (l + h) / 2;
            if (arr[mid] >= x)
                h = mid - 1;
            else
                l = mid + 1;
        }
        return l;
    }
     
	
	 static int UpperBound(int a[], int x)
	  {// x is the key or target value
	    int l=-1,r=a.length;
	    while(l+1<r) {
	       int m=(l+r)>>>1;
	       if(a[m]<=x) l=m;
	       else r=m;
	    }
	    return l+1;
	 }
	 static class DisjointUnionSets
	 {
	    int[] rank, parent;
	    int n;
	    // Constructor
	    public DisjointUnionSets(int n)
	    {
	        rank = new int[n];
	        parent = new int[n];
	        this.n = n;
	        makeSet();
	    }
	    // Creates n sets with single item in each
	    void makeSet()
	    {
	        for (int i = 0; i < n; i++)
	            parent[i] = i;
	    }
	    int find(int x)
	    {
	        if (parent[x] != x) {
	            parent[x] = find(parent[x]);
	        }
	        return parent[x];
	    }
	    // Unites the set that includes x and the set
	    // that includes x
	    void union(int x, int y)
	    {
	        int xRoot = find(x), yRoot = find(y);
	        if (xRoot == yRoot)
	            return;
	        if (rank[xRoot] < rank[yRoot])
	            parent[xRoot] = yRoot;
	        else if (rank[yRoot] < rank[xRoot])
	         parent[yRoot] = xRoot;
	        else // if ranks are the same
	        {
	         parent[yRoot] = xRoot;
	            rank[xRoot] = rank[xRoot] + 1;
	        }
	    }
	 }

	 
//	static class countClass{
//		int cnt;
//		public countClass() {
//			this.cnt=0;
//			// TODO Auto-generated constructor stub
//		}
//	}

	 
	 
	static class Graph
	  {
	        int v;
	        ArrayList<Integer> list[];
	        Graph(int v)
	        {
	            this.v=v;
	            list=new ArrayList[v+1];
	            for(int i=1;i<=v;i++)
	                list[i]=new ArrayList<Integer>();
	        }
	        void addEdge(int a, int b)
	        {
	            this.list[a].add(b);
	        }
	    }
	
//	static class GraphMap{
//		Map<String,ArrayList<String>> graph;
//		GraphMap() {
//			// TODO Auto-generated constructor stub
//			graph=new HashMap<String,ArrayList<String>>();
//			
//		}
//		void addEdge(String a,String b)
//		{
//			if(graph.containsKey(a))
//			this.graph.get(a).add(b);
//			else {
//				this.graph.put(a, new ArrayList<>());
//				this.graph.get(a).add(b);
//			}
//		}
//	}
//	static void dfsMap(GraphMap g,HashSet<String> vis,String src,int ok)
//	{
//		vis.add(src);
//		
//		if(g.graph.get(src)!=null)
//		{
//			for(String each:g.graph.get(src))
//			{
//				if(!vis.contains(each))
//				{
//					dfsMap(g, vis, each, ok+1);
//				}
//			}
//		}
//		
//		cnt=Math.max(cnt, ok);
//	}
	static double sum[];
	static long cnt;
	static void DFS(Graph g, boolean[] visited, int u)
		{
	        visited[u]=true;
	        
	        for(int i=0;i<g.list[u].size();i++)
	        {
	            int v=g.list[u].get(i);
	            
	            if(!visited[v])
	            {
	            	cnt=cnt*2;
	            	DFS(g, visited, v);
	            
	            }
	            
	        }
	       

	  } 
	
	
	  
	 static class Pair
	    {
	       int x,y;
	       Pair(int x,int y)
	        {
	           this.x=x;
	           this.y=y;
	        }
	       
	       
	       
	    }
	   
	static long sum_array(int a[])
	 {
	    int n=a.length;
	    long sum=0;
	    for(int i=0;i<n;i++)
	     sum+=a[i];
	    return sum;
	 }
	static long sum_array(long a[])
	 {
	    int n=a.length;
	    long sum=0;
	    for(int i=0;i<n;i++)
	     sum+=a[i];
	    return sum;
	 }

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

	static void reverse_array(int a[])
	 {
	    int n=a.length;
	    int i,t; 
	    for (i = 0; i < n / 2; i++) { 
	            t = a[i]; 
	            a[i] = a[n - i - 1]; 
	            a[n - i - 1] = t; 
	        } 
	 }
	static void reverse_array(long a[])
	 {
	    int n=a.length;
	    int i; long t; 
	    for (i = 0; i < n / 2; i++) { 
	            t = a[i]; 
	            a[i] = a[n - i - 1]; 
	            a[n - i - 1] = t; 
	        } 
	 }
	 static long modInverse(long a, long m)
		    {
		        long g = gcd(a, m);
		       
		          return   power(a, m - 2, m);
		        
		    }
	static long power(long x, long y, long m)
		    {
		        if (y == 0)
		            return 1;
		        long p = power(x, y / 2, m) % m;
		        p = (int)((p * (long)p) % m);
		        if (y % 2 == 0)
		            return p;
		        else
		            return (int)((x * (long)p) % m);
		    }
	static long gcd(long a, long b) 
	    { 
	        if (a == 0) 
	            return b; 
	          
	        return gcd(b%a, a); 
	    } 
	static int gcd(int a, int b) 
	    { 
	        if (a == 0) 
	            return b; 
	          
	        return gcd(b%a, a); 
	    } 

	   static class FastReader{
	 
	        byte[] buf = new byte[2048];
	        int index, total;
	        InputStream in;
	 
	        FastReader(InputStream is) {
	            in = is;
	        }
	 
	        int scan() throws IOException {
	            if (index >= total) {
	                index = 0;
	                total = in.read(buf);
	                if (total <= 0) {
	                    return -1;
	                }
	            }
	            return buf[index++];
	        }
	 
	        String next() throws IOException {
	            int c;
	            for (c = scan(); c <= 32; c = scan());
	            StringBuilder sb = new StringBuilder();
	            for (; c > 32; c = scan()) {
	                sb.append((char) c);
	            }
	            return sb.toString();
	        }
	 
	        int nextInt() throws IOException {
	            int c, val = 0;
	            for (c = scan(); c <= 32; c = scan());
	            boolean neg = c == '-';
	            if (c == '-' || c == '+') {
	                c = scan();
	            }
	            for (; c >= '0' && c <= '9'; c = scan()) {
	                val = (val << 3) + (val << 1) + (c & 15);
	            }
	            return neg ? -val : val;
	        }
	 
	        long nextLong() throws IOException {
	            int c;
	            long val = 0;
	            for (c = scan(); c <= 32; c = scan());
	            boolean neg = c == '-';
	            if (c == '-' || c == '+') {
	                c = scan();
	            }
	            for (; c >= '0' && c <= '9'; c = scan()) {
	                val = (val << 3) + (val << 1) + (c & 15);
	            }
	            return neg ? -val : val;
	        }
	    }
	   
	    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') 
	                    break; 
	                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(); 
	        } 
	    }
	  static  PrintWriter out=new PrintWriter(System.out);
	  static int int_max=Integer.MAX_VALUE;
	  static int int_min=Integer.MIN_VALUE;
	  static long long_max=Long.MAX_VALUE;
	  static long long_min=Long.MIN_VALUE;

}




