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
h, w, k = map(int, input().split())
n = h*w
x1, y1, x2, y2 = map(lambda x: int(x)-1, input().split())
fld = ''.join([input()for _ in range(h)])


def bfs(init_v):
    next_v = deque([init_v])
    dist = [-1]*n
    dist[init_v] = 0
    while next_v:
        v = next_v.popleft()
        i, j = divmod(v, w)
        dirc = [(-1, 0), (0, 1), (1, 0), (0, -1)]
        for di, dj in dirc:
            for a in range(1, k+1):
                x, y = i+di*a, j+dj*a
                if x < 0 or h <= x or y < 0 or w <= y:
                    break
                v2 = x*w+y
                if fld[v2] == '@':
                    break
                if dist[v2] != -1 and dist[v2] <= dist[v]:
                    break
                if dist[v2] != -1:
                    continue
                dist[v2] = dist[v]+1
                next_v.append(v2)
    return dist


dist = bfs(x1*w+y1)
print(dist[x2*w+y2])