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
printn = lambda x: print(x,end='')
inn = lambda : int(input())
inl   = lambda: list(map(int, input().split()))
inm   = lambda:      map(int, input().split())
ins = lambda : input().strip()
DBG = True # and False
BIG = 10**18
R = 10**9 + 7
#R = 998244353

def ddprint(x):
  if DBG:
    print(x)

h,w,k = inm()
x1,y1,x2,y2 = inm()
x1 -= 1
y1 -= 1
x2 -= 1
y2 -= 1
c = []
for i in range(h):
    c.append(ins())
d = [[-1]*w for i in range(h)]
q = deque([(x1,y1)])
d[x1][y1] = 0
dir = [(0,1),(0,-1),(1,0),(-1,0)]
while len(q)>0:
    x,y = q.popleft()
    dd = d[x][y]+1
    for dx,dy in dir:
        for i in range(1,k+1):
            xx = x+i*dx
            yy = y+i*dy
            if xx<0 or h<=xx or yy<0 or w<=yy or \
               (d[xx][yy]>=0 and d[xx][yy]<dd) or c[xx][yy]=='@':
                break
            if d[xx][yy] == dd:
                continue
            d[xx][yy] = dd
            q.append((xx,yy))
            if xx==x2 and yy==y2:
                print(dd)
                exit()
print(-1)