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:
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;

//template
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
typedef long long int ll;
const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12;
template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
//end

typedef pair<int,int> P;
typedef pair<int,P> T;

int dx[]={1,-1,0,0},dy[]={0,0,1,-1};

int main(){
   int h,w,k; cin>>h>>w>>k;
   int x1,y1,x2,y2; cin>>x1>>y1>>x2>>y2; x1--; y1--; x2--; y2--;
   vector<vector<char>> g(h,vector<char>(w));
   rep(i,0,h)rep(j,0,w)cin>>g[i][j];
   vector<vector<int>> dist(h,vector<int>(w,inf));
   dist[x1][y1]=0; queue<P> que; que.push(P(x1,y1));
   while(!que.empty()){
      auto [nx,ny]=que.front(); que.pop();
      rep(i,0,4)rep(add,1,k+1){
         int tx=nx+dx[i]*add,ty=ny+dy[i]*add;
         if(tx<0 or tx>=h or ty<0 or ty>=w or g[tx][ty]=='@')break;
         if(dist[tx][ty]<=dist[nx][ny])break;
         if(dist[tx][ty]==inf){
            dist[tx][ty]=dist[nx][ny]+1; que.push(P(tx,ty));
         }
      }
   }
   if(dist[x2][y2]==inf)puts("-1");
   else cout<<dist[x2][y2]<<endl;
   return 0;
}