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 PYTHON3):

Solution:
import sys
input = sys.stdin.readline

h,w,k=map(int, input().split())
x1,y1,x2,y2=map(int, input().split())
x1-=1;y1-=1;x2-=1;y2-=1
c=[input() for _ in range(h)]
INF=10**14
dp=[[INF for _ in range(w)] for _ in range(h)]
dp[x1][y1]=0
from collections import deque
q=deque()

q.append((x1,y1))
dxy=[(1,0),(0,1),(-1,0),(0,-1)]

while q:
    x,y=q.popleft()
    for dx,dy in dxy:
        for j in range(1,k+1):
            if not 0<=x+dx*j<h:break
            if not 0<=y+dy*j<w:break
            if c[x+dx*j][y+dy*j]=='@':break
            if dp[x+dx*j][y+dy*j]>dp[x][y]+1:
                dp[x+dx*j][y+dy*j]=dp[x][y]+1
                q.append((x+dx*j,y+dy*j))
            elif dp[x+dx*j][y+dy*j]==dp[x][y]+1:continue###
            elif dp[x+dx*j][y+dy*j]<=dp[x][y]:break###
    
            
            if x+dx*j==x2 and y+dy*j==y2:
                print(dp[x2][y2])
                exit()

        
print(-1)