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
inf=1000002
sys.setrecursionlimit(inf)
from collections import deque
h,w,k=map(int,input().split())
x1,y1,x2,y2=map(int,input().split())
c=[input() for i in range(h)]
dp=[[inf if c[i][j]=="." else -1 for j in range(w)] for i in range(h)]
now=deque([[x1-1,y1-1]])
dp[x1-1][y1-1]=0
def bfs(d):
    global dp,now
    l=len(now)
    if l==0:
        return
    dp_sub=deque()
    cand=set()
    for i in range(l):
        x,y=now.popleft()
        for j in range(1,min(k+1,w-y)):
            if dp[x][y+j]==inf:
                dp_sub.append([x,y+j,d])
                cand.add((x,y+j))
            else:
                break
        for j in range(1,min(k+1,y+1)):
            if dp[x][y-j]==inf:
                dp_sub.append([x,y-j,d])
                cand.add((x,y-j))
            else:
                break
        for j in range(1,min(k+1,h-x)):
            if dp[x+j][y]==inf:
                dp_sub.append([x+j,y,d])
                cand.add((x+j,y))
            else:
                break
        for j in range(1,min(k+1,x+1)):
            if dp[x-j][y]==inf:
                dp_sub.append([x-j,y,d])
                cand.add((x-j,y))
            else:
                break
    while dp_sub!=deque([]):
        e=dp_sub.popleft()
        dp[e[0]][e[1]]=e[2]
    for i in cand:
        now.append(i)
    bfs(d+1)
bfs(1)
print(dp[x2-1][y2-1] if dp[x2-1][y2-1]!=inf else -1)