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.io.*;
import java.util.*;

public class Practice
{
//	static final long mod=7420738134811L;
	static int mod=1000000007;
	static final int size=1001;
	static FastReader sc=new FastReader(System.in);
//	static Reader sc=new Reader();
	static  PrintWriter out=new PrintWriter(System.out);
	static long[] factorialNumInverse;
	static long[] naturalNumInverse;	
	static long[] fact;
	public static void main(String[] args) throws IOException
	{
//		System.setIn(new FileInputStream("input.txt"));
//		System.setOut(new PrintStream("output.txt"));
//		naturalNumInverse=new long[size];
//		factorialNumInverse=new long[size];
//		fact=new long[size];
//		factorial(mod);
//		InverseofNumber(mod);
//		InverseofFactorial(mod);
		int t=1;
		t=sc.nextInt();
		while(t-->0)
		{
			solve();
//			sb.append("\n");
		}
//		out.print(sb);
		out.close();
		out.flush();
	}
	static void solve() throws IOException
	{
		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);
			}
		//store position of every sight
		int pos[][]=new int[n][m];
		int i=0,j=0;
		//for every sight find the first row in wich it appears and the last pos of it in it
//				sight			row			positions
		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();
//				out.println(position);
//				out.println(position.getKey()*m+col);
				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);
	}
	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 class Pair implements Cloneable
	{
		int x,y;
		Pair(int a,int b)
		{
			this.x=a;
			this.y=b;
		}
		@Override
		public String toString() 
		{
			return "("+x+","+(y)+")";
		}
		@Override
		protected Pair clone() throws CloneNotSupportedException {
			return new Pair(this.x,this.y);
		}
	}
	static class Tuple implements Cloneable
	{
		int x,y,z;
		Tuple(int a,int b,int c)
		{
			this.x=a;
			this.y=b;
			this.z=c;
		}
		@Override
		public String toString() 
		{
			return "("+x+","+y+","+z+")";
		}
		@Override
		protected Tuple clone() throws CloneNotSupportedException {
			return new Tuple(this.x,this.y,this.z);
		}
	}
	static void arraySort(int arr[])
	{
		ArrayList<Integer> a=new ArrayList<Integer>();
		for (int i = 0; i < arr.length; i++) {
			a.add(arr[i]);
		}
		Collections.sort(a);
		for (int i = 0; i < arr.length; i++) {
			arr[i]=a.get(i);
		}
	}
	static void arraySort(long arr[])
	{
		ArrayList<Long> a=new ArrayList<Long>();
		for (int i = 0; i < arr.length; i++) {
			a.add(arr[i]);
		}
		Collections.sort(a);
		for (int i = 0; i < arr.length; i++) {
			arr[i]=a.get(i);
		}
	}
	public static void InverseofNumber(int p)
	{
	    naturalNumInverse[0] = naturalNumInverse[1] = 1;
	    for(int i = 2; i < size; i++)
	        naturalNumInverse[i] = naturalNumInverse[p % i] * (long)(p - p / i) % p;
	}
	// Function to precompute inverse of factorials
	public static void InverseofFactorial(int p)
	{
	    factorialNumInverse[0] = factorialNumInverse[1] = 1;
	    // pre-compute inverse of natural numbers
	    for(int i = 2; i < size; i++)
	        factorialNumInverse[i] = (naturalNumInverse[i] * factorialNumInverse[i - 1]) % p;
	}
	// Function to calculate factorial of 1 to 200001
	public static void factorial(int p)
	{
	    fact[0] = 1;
	    for(int i = 1; i < size; i++)
	        fact[i] = (fact[i - 1] * (long)i) % p;
	}
	 
	// Function to return nCr % p in O(1) time
	public static long Binomial(int N, int R, int p)
	{
	     
	    // n C r = n!*inverse(r!)*inverse((n-r)!)
	    long ans = ((fact[N] * factorialNumInverse[R]) % p * factorialNumInverse[N - R]) % p;
	     
	    return ans;
	}
	static int findXOR(int x)	//from 0 to x
	{
		if(x<0)
			return 0;
		if(x%4==0)
			return x;
		if(x%4==1)
			return 1;
		if(x%4==2)
			return x+1;
		return 0;
	}
	static boolean isPrime(long x)
	{
		if(x==1)
			return false;
		if(x<=3)
			return true;
		if(x%2==0 || x%3==0)
			return false;
		for(int i=5;i<=Math.sqrt(x);i+=2)
			if(x%i==0)
				return false;
		return true;
	}
	static long gcd(long a,long b)
	{
		return (b==0)?a:gcd(b,a%b);
	}
	static int gcd(int a,int b)
	{
		return (b==0)?a:gcd(b,a%b);
	}
	static class UnionFind
	{
		  private int size;
		  private int[] sz;
		  private int[] parent;
		  private int numComponents;
		  public UnionFind(int size) 
		  {
		    if (size <= 0) throw new IllegalArgumentException("Size <= 0 is not allowed");
		    this.size = numComponents = size;
		    sz = new int[size];
		    parent = new int[size];
		    for (int i = 0; i < size; i++) 
		    {
		      parent[i] = i; 									// Link to itself (self root)
		      sz[i] = 1;								// Each component is originally of size one
		    }
		  }
		  public int find(int p) 
		  {
		    int root = p;
		    while (root != parent[root])
		    	root = parent[root];
		    while (p != root)
		    {
		      int next = parent[p];
		      parent[p] = root;
		      p = next;
		    }
		    return root;
		  }
		  public void makeParent(int p,int u)
		  {
			  parent[p]=u;
		  }
		  public boolean isConnected(int p, int q) 
		  {
		    return find(p) == find(q);
		  }
		  public int componentSize(int x) 
		  {
		    return sz[find(x)];
		  }
		  public int size() 
		  {
		    return size;
		  }
		  public int components() 
		  {
		    return numComponents;
		  }
		  public void unify(int p, int q) 
		  {
		    int root1 = find(p);
		    int root2 = find(q);
		    if(root1==root2)
		    {
		    	return;
		    }
		    else if (sz[root1] < sz[root2]) 
		    {
		    	parent[root1] = root2;
		    	sz[root2] += sz[root1];
		    	sz[root1] = 0;
		  } 
		    else 
		    {
		    	parent[root2] = root1;
		    	sz[root1] += sz[root2];
		    	sz[root2] = 0;
		    }
		    numComponents--;
		  }
		  void calc()
		  {
			  for(int i=0;i<size;i++)
				  find(i);
			  
		  }
	}
	static class Node
	{
		int vertex,dp;
		ArrayList<Edge> adj;
		ArrayList<Node> parent;
		Node(int v)
		{
			vertex=v;
			adj=new ArrayList<Edge>();
			parent=new ArrayList<Node>();
			dp=0;
		}
		@Override
		public String toString() 
		{
			return vertex+" ";
		}
	}
	static class Edge
	{
		Node to;
		int cost;
		Edge(Node t,int c)
		{
			this.to=t;
			this.cost=c;
		}
		@Override
		public String toString() {
			return "("+to.vertex+","+cost+") ";
		}
	}
	static long power(long x, long y)
	  {
	    long res = 1; 
	    x = x % mod; 
	    if (x == 0)
	      return 0; 
	    while (y > 0)
	    {
	    	if ((y & 1) != 0)
	    		res = (res * x) % mod;
	    	
	    	y = y >> 1; // y = y/2
	    	x = (x * x) % mod;
	    }
	    return res;
	  }
	static long binomialCoeff(long n, long k)
    {
        long res = 1;
//        if(k>n)
//        	return 0;
        // Since C(n, k) = C(n, n-k)
        if (k > n - k)
            k = n - k;
 
        // Calculate value of
        // [n * (n-1) *---* (n-k+1)] / [k * (k-1) *----* 1]
        for (long i = 0; i < k; ++i) {
            res *= (n - i);
            res /= (i + 1);
        }
 
        return res;
    }
	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') {
                    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 void printarray(int arr[])
        {
        	for (int i = 0; i < arr.length; i++)
				System.out.print(arr[i]+" ");
        	System.out.println();
        }
    }
}
//
//int n=sc.nextInt(),m=sc.nextInt();
//ArrayList<Pair> arr=new ArrayList<Pair>();
//for(int i=0;i<n*m;i++)
//	arr.add(new Pair(i,sc.nextInt()));
//Collections.sort(arr,new Comparator<Pair>() {
//	@Override
//	public int compare(Practice.Pair a, Practice.Pair b) {
//		int sightdiff=a.y-b.y;
//		if(sightdiff!=0)
//			return sightdiff;
//		else
//			return b.x-a.x;
//	}
//});
//int pos[]=new int[n*m];
//for(int i=0;i<n*m;i++)
//	pos[arr.get(i).x]=i;
//out.println(arr);
//out.println(Arrays.toString(pos));
//segment help=new segment(n*m);
//long ans=0;
//for(int i=0;i<n*m;i++)
//{
//	int start=(pos[i]/m)*m;
//	int incov=help.find(start,pos[i]-1);
////	out.println(start+" "+arr.get(i).x+" "+incov);
//	ans+=incov;
//	help.doUP(pos[i]);
//}
//out.println(ans);







