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:
h,w,k = map(int,input().split())
x1,y1,x2,y2 = map(int,input().split())
c = []
for i in range(h):
  c.append(list(input()))

q = [(1,x1-1,y1-1)]
c[x1-1][y1-1] = 0
while(q):
  qq = []
  for a,x,y in q:
    for dx,dy in ((0,-1),(0,1),(-1,0),(1,0)):
      for kk in range(1,k+1):
        xx = x+dx*kk
        yy = y+dy*kk
        if not (0 <= xx < h) or not (0 <= yy < w) or c[xx][yy] == '@' or (c[xx][yy] != '.' and c[xx][yy] < a):
          break
        if c[xx][yy] == '.' or (c[xx][yy] != '.' and c[xx][yy] > a):
          c[xx][yy] = a
          qq.append((a+1,xx,yy))
  #print(qq)
  q = qq[:]

print(-1 if c[x2-1][y2-1] == '.' else c[x2-1][y2-1])
#print(c)