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.*;

public class Main {
	static class Path {
		int dir;
		int step;
		int move;
		int y, x;
		
		public Path(int dir, int step, int move, int y, int x) {
			this.dir = dir;
			this.step = step;
			this.move = move;
			this.y = y;
			this.x = x;
		}
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int H = sc.nextInt();
		int W = sc.nextInt();
		int K = sc.nextInt();
		int y1 = sc.nextInt()-1;
		int x1 = sc.nextInt()-1;
		int y2 = sc.nextInt()-1;
		int x2 = sc.nextInt()-1;

		char[][] m = new char[H][];
		for(int i=0; i<H; i++)
			m[i] = sc.next().toCharArray();

		long[][][] best = new long[H][W][4];
		for(int i=0; i<H; i++)
			for(int j=0; j<W; j++)
				Arrays.fill(best[i][j], Long.MAX_VALUE);
		
		final int[] dx = {0, 1, 0, -1};
		final int[] dy = {1, 0, -1, 0};
		
		PriorityQueue<Path> q = new PriorityQueue<Path>(new Comparator<Path>() {
			public int compare(Path p1, Path p2) {
				if(p1.step==p2.step)
					return Integer.compare(p1.move, p2.move);
				else
					return Integer.compare(p1.step, p2.step);
			}
		});
		
		for(int d=0; d<4; d++) {
			q.add(new Path(d, 1, 0, y1, x1));
		}
		
		while(!q.isEmpty()) {
			Path cur = q.poll();
			
			if(best[cur.y][cur.x][cur.dir] <= cur.step*(K+1)+cur.move)
				continue;
			best[cur.y][cur.x][cur.dir] = cur.step*(K+1)+cur.move;
			
			for(int d=0; d<4; d++) {
				int ny = cur.y + dy[d];
				int nx = cur.x + dx[d];
				if(0<=ny && ny<H && 0<=nx && nx<W &&m[ny][nx]=='.') {
					int nextStep = cur.step;
					int nextMove = cur.move;
					if(d==cur.dir && nextMove<K) {
						nextMove++;
					} else {
						nextStep++;
						nextMove = 1;
					}
					if(best[ny][nx][d] > nextStep*(K+1)+nextMove)
						q.add(new Path(d, nextStep, nextMove, ny, nx));
				}
			}
		}
		long ans = Long.MAX_VALUE;
		for(int d=0; d<4; d++)
			ans = Math.min(ans, best[y2][x2][d]);
		System.out.println(ans < Long.MAX_VALUE ? ans/(K+1) : -1);

		sc.close();
	}
}