Problem: Snuke, a water strider, lives in a rectangular pond that can be seen as a grid with H east-west rows and W north-south columns. Let (i,j) be the square at the i-th row from the north and j-th column from the west.

Some of the squares have a lotus leaf on it and cannot be entered. The square (i,j) has a lotus leaf on it if c_{ij} is `@`, and it does not if c_{ij} is `.`.

In one stroke, Snuke can move between 1 and K squares (inclusive) toward one of the four directions: north, east, south, and west. The move may not pass through a square with a lotus leaf. Moving to such a square or out of the pond is also forbidden.

Find the minimum number of strokes Snuke takes to travel from the square (x_1,y_1) to (x_2,y_2). If the travel from (x_1,y_1) to (x_2,y_2) is impossible, point out that fact.

Constraints

* 1 \leq H,W,K \leq 10^6
* H \times W \leq 10^6
* 1 \leq x_1,x_2 \leq H
* 1 \leq y_1,y_2 \leq W
* x_1 \neq x_2 or y_1 \neq y_2.
* c_{i,j} is `.` or `@`.
* c_{x_1,y_1} = `.`
* c_{x_2,y_2} = `.`
* All numbers in input are integers.

Input

Input is given from Standard Input in the following format:


H W K
x_1 y_1 x_2 y_2
c_{1,1}c_{1,2} .. c_{1,W}
c_{2,1}c_{2,2} .. c_{2,W}
:
c_{H,1}c_{H,2} .. c_{H,W}


Output

Print the minimum number of strokes Snuke takes to travel from the square (x_1,y_1) to (x_2,y_2), or print `-1` if the travel is impossible.

Examples

Input

3 5 2
3 2 3 4
.....
.@..@
..@..


Output

5


Input

1 6 4
1 1 1 6
......


Output

2


Input

3 3 1
2 1 2 3
.@.
.@.
.@.


Output

-1

Solution (in JAVA):

Solution:
import java.util.*;		
import java.util.function.Function;
import java.util.stream.Collectors;
import java.io.*;
import java.math.*;
public class Main{
	static public void main(String args[])throws IOException{
		int tt=1;
		StringBuilder sb=new StringBuilder();
		for(int ttt=1;ttt<=tt;ttt++){
			int n=i();
			int m=i();
			int k=i();
			int x1=i()-1;
			int y1=i()-1;
			int x2=i()-1;
			int y2=i()-1;
			char[][] a=new char[n][m];
			for(int i=0;i<n;i++){
				String s=s();
				for(int j=0;j<m;j++){
					a[i][j]=s.charAt(j);
				}
			}
			Queue<Pair> queue=new LinkedList<>();
			queue.add(new Pair(x1,y1));
			int[] dx=new int[]{1,-1,0,0};
			int[] dy=new int[]{0,0,1,-1};
			boolean[][] visited=new boolean[n][m];
			int[][] dis=new int[n][m];
			for(int i=0;i<n;i++){
				Arrays.fill(dis[i],Integer.MAX_VALUE);
			}
			visited[x1][y1]=true;
			dis[x1][y1]=0;
			while(queue.isEmpty()==false){
				Pair p=queue.poll();
				int u=p.x;
				int v=p.y;
				int count=0;
				for(int i=u+1;i<n;i++){
					if(visited[i][v]==false && dis[i][v]>dis[u][v]+1 && count<k && a[i][v]=='.'){
						dis[i][v]=dis[u][v]+1;
						visited[i][v]=true;
						queue.add(new Pair(i,v));
					}else if(a[i][v]!='.' || count>=k || dis[i][v]<dis[u][v]+1){
						break;
					}
					count++;
				}
				count=0;
				for(int i=u-1;i>=0;i--){
					if(visited[i][v]==false && dis[i][v]>dis[u][v]+1 && count<k && a[i][v]=='.'){
						dis[i][v]=dis[u][v]+1;
						visited[i][v]=true;
						queue.add(new Pair(i,v));
					}else if(a[i][v]!='.' || count>=k || dis[i][v]<dis[u][v]+1){
						break;
					}
					count++;
				}
				count=0;
				for(int i=v+1;i<m;i++){
					if(visited[u][i]==false && dis[u][i]>dis[u][v]+1 && count<k && a[u][i]=='.'){
						dis[u][i]=dis[u][v]+1;
						visited[u][i]=true;
						queue.add(new Pair(u,i));
					}else if(a[u][i]!='.' || count>=k || dis[u][i]<dis[u][v]+1){
						break;
					}
					count++;
				}
				count=0;
				for(int i=v-1;i>=0;i--){
					if(visited[u][i]==false && dis[u][i]>dis[u][v]+1 && count<k && a[u][i]=='.'){
						dis[u][i]=dis[u][v]+1;
						visited[u][i]=true;
						queue.add(new Pair(u,i));
					}else if(a[u][i]!='.' || count>=k || dis[u][i]<dis[u][v]+1){
						break;
					}
					count++;
				}
			}
			if(dis[x2][y2]==Integer.MAX_VALUE){
				pln("-1");
			}else{
				pln(dis[x2][y2]+"");
			}
		}
		System.out.print(sb.toString());
	}
	static InputReader in=new InputReader(System.in);
	static OutputWriter out=new OutputWriter(System.out);
	static ArrayList<ArrayList<Integer>> graph;
	static int mod=1000000007;
	static class Pair{
		int x;
		int y;
		Pair(int x,int y){
			this.x=x;
			this.y=y;
		}
	/*	@Override
        public int compareTo(Pair o) {
            if (value != o.value) {
                return Integer.compare(value, o.value);
            }
            return Integer.compare(id, o.id);
        }*/
	/*	@Override
		public int hashCode() 
		{ 
			final int temp = 14; 
			int ans = 1; 
			ans =x*31+y*13; 
			return (int)ans;
		}*/ 
   /*    @Override
        public boolean equals(Object o) 
        { 
            if (this == o) { 
                return true; 
            } 
            if (o == null) { 
                return false; 
            } 
            if (this.getClass() != o.getClass()) { 
                return false; 
            } 
            Pair other = (Pair)o; 
            if (this.x != other.x || this.y!=other.y) { 
                return false; 
            } 
            return true; 
        }*/
	}
	public static int[] sort(int[] a){
		int n=a.length;
		ArrayList<Integer> ar=new ArrayList<>();
		for(int i=0;i<a.length;i++){
			ar.add(a[i]);
		}
		Collections.sort(ar);
		for(int i=0;i<n;i++){
			a[i]=ar.get(i);
		}
		return a;
	}
	public static long pow(long a, long b){
        long result=1;
        while(b>0){
            if (b % 2 != 0){
                result=(result*a)%mod;
                b--;
            } 
            a=(a*a)%mod;
            b /= 2;
        }   
        return result;
    }
	public static long gcd(long a, long b){
        if (a == 0){
            return b;
		}
        return gcd(b%a, a);
    }
	public static long lcm(long a, long b){
		return a*(b/gcd(a,b));
	}
	public static long l(){
		String s=in.String();
		return Long.parseLong(s);
	}
	public static void pln(String value){
		System.out.println(value);
	}
	public static int i(){
		return in.Int();
	}
	public static String s(){
		return in.String();
	}
}
class InputReader 
{
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;
	public InputReader(InputStream stream) {
		this.stream = stream;
	}
	public int read() {
		if (numChars== -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}
	public int Int() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
	public String String() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	} 
	public boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	} 
	public String next() {
		return String();
	} 
	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}
class OutputWriter {
	private final PrintWriter writer;
	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}
	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}
	public void print(Object...objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}
	public void printLine(Object...objects) {
		print(objects);
		writer.println();
	}
	public void close() {
		writer.close();
	}
	public void flush() {
		writer.flush();
	}
 }
class IOUtils {
	public static int[] readIntArray(InputReader in, int size) {
		int[] array = new int[size];
		for (int i = 0; i < size; i++)
			array[i] = in.Int();
		return array;
	}
}