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 CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=1e5+5,inf=0x3f3f3f3f;
#define mst(a) memset(a,0,sizeof a)
#define lx x<<1
#define rx x<<1|1
#define reg register
#define PII pair<int,int>
#define fi first 
#define se second
int H,W,K;
int d[4][2]={0,1,0,-1,1,0,-1,0};
int main(){
	scanf("%d%d%d",&H,&W,&K);
	vector<string>S(H);
	int sx,sy,ex,ey;
	scanf("%d%d%d%d",&sx,&sy,&ex,&ey);
	sx--,sy--,ex--,ey--;
	for(int i=0;i<H;i++) cin>>S[i];
	vector<vector<int> >a(H,vector<int>(W,1e9));
	queue<PII>q;
	a[sx][sy]=0;
	q.push({sx,sy});
	while(!q.empty()){
		 int x=q.front().fi,y=q.front().se;
		 q.pop();
		 for(int i=0;i<4;i++){
		 	 int nx=x,ny=y;
		 	 int tmp=a[x][y]+1;
		 	 for(int k=1;k<=K;k++){
		 	 	  nx+=d[i][0],ny+=d[i][1];
		 	 	  if(nx<0||nx>=H||ny<0||ny>=W||S[nx][ny]=='@'||a[nx][ny]<tmp) break;
		 	 	  if(a[nx][ny]>tmp){
		 	 	  		a[nx][ny]=tmp;
		 	 	  		q.push({nx,ny}); 
					}
			  }
		 }
	}
	printf(a[ex][ey]==1e9?"-1":"%d\n",a[ex][ey]);
	return 0;
}