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;
using ll = long long;
using P = pair<int,int>;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define all(v) v.begin(), v.end()

const ll INF = 1e18;

int main() {
    int h,w,k,x,y,nx,ny,K;
    cin >> h >> w >> k;
    int a,b,c,d;
    cin >> a >> b >> c >> d;
    a--;b--;c--;d--;
    vector<string> g(h);
    rep(i,h) cin >> g[i];
    vector<int> dx = {1,-1,0,0};
    vector<int> dy = {0,0,1,-1};
    vector<vector<ll>> depth(h,vector<ll>(w,INF));
    queue<P> q;
    q.push(make_pair(b,a));
    depth[a][b] = 0;
    while (!q.empty()){
        x = q.front().first;
        y = q.front().second;
        q.pop();
        if (x==d and y==c) break;
        rep(i,4){
            nx = x;
            ny = y;
            K = k;
            while (K--){
                nx += dx[i];
                ny += dy[i];
                if (0<=nx and nx<w and 0<=ny and ny<h and g[ny][nx] != '@'
                and depth[ny][nx] > depth[y][x]){
                    if (depth[ny][nx] != depth[y][x] + 1){
                        depth[ny][nx] = depth[y][x] + 1;
                        q.push(make_pair(nx,ny));
                    } 
                }
                else break;
            }
        }
    }
    if (depth[c][d] == INF) cout << -1 << endl;
    else cout << depth[c][d] << endl;
}