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 queue

H,W,K = map(int,input().split())
x1,y1,x2,y2 = map(int,input().split())

li = [list(input()) for _ in range(H)]
cnt = [[10**10 for _ in range(W)] for _ in range(H)]
cnt2 = [[10**10 for _ in range(W)] for _ in range(H)]



xy = [[1,0], [0,1], [-1,0], [0,-1]]

q = queue.Queue()
q.put([x1-1,y1-1,0])
cnt[x1-1][y1-1] = 0

while not(q.empty()):
    mm = q.get()
    x = mm[0]
    y = mm[1]
    cst = mm[2]

    for i in range(4):
        # print(x,y)
        for j in range(1,K+1):
            nx = x+xy[i][0]*j
            ny = y+xy[i][1]*j
            # print(nx,ny)
            
            if nx>=0 and nx<H and ny>=0 and ny<W and li[nx][ny]==".":
                if cnt[nx][ny]!=10**10 and cnt[nx][ny]<cst+1:
                    break
                elif cnt[nx][ny]!=10**10:
                    continue
                else:
                    cnt[nx][ny] = cst + 1
                    q.put([nx,ny,cst+1])
            else:
                break

if cnt[x2-1][y2-1]==10**10:
    print(-1)
else:
    print(cnt[x2-1][y2-1])

# for i in range(H):
#     for j in range(W):
#         print("{:>10}".format(cnt[i][j]),end="")
#     print()