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:
from collections import deque
import sys

int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def MI1(): return map(int1, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]

def main():
    inf=10**9
    h,w,k=MI()
    x1,y1,x2,y2=MI1()
    aa=[[0 if c=="@" else inf for c in SI()] for _ in range(h)]
    #p2D(aa)

    aa[x1][y1]=0
    q=deque()
    q.append((x1,y1,0))
    while q:
        x,y,d=q.popleft()
        for nx in range(x+1,min(x+k+1,h)):
            if aa[nx][y] == d + 1:continue
            if aa[nx][y]<d+1:break
            aa[nx][y]=d+1
            q.append((nx,y,d+1))
        for nx in range(x-1,max(x-k-1,-1),-1):
            if aa[nx][y] == d + 1:continue
            if aa[nx][y]<d+1:break
            aa[nx][y]=d+1
            q.append((nx,y,d+1))
        for ny in range(y+1,min(y+k+1,w)):
            if aa[x][ny] == d + 1:continue
            if aa[x][ny]<d+1:break
            aa[x][ny]=d+1
            q.append((x,ny,d+1))
        for ny in range(y-1,max(y-k-1,-1),-1):
            if aa[x][ny] == d + 1:continue
            if aa[x][ny]<d+1:break
            aa[x][ny]=d+1
            q.append((x,ny,d+1))
        #p2D(aa)
        #print()

    ans=aa[x2][y2]
    if ans==inf:print(-1)
    else:print(ans)

main()