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 sys
from collections import deque

sys.setrecursionlimit(10 ** 7)
rl = sys.stdin.readline


def solve():
    H, W, K = map(int, rl().split())
    sy, sx, gy, gx = map(lambda n: int(n) - 1, rl().split())
    c = [rl().rstrip() for _ in range(H)]
    
    INF = 10 ** 10
    cost = [[INF] * W for _ in range(H)]
    cost[sy][sx] = 0
    que = deque([(sy, sx)])
    while que:
        cy, cx = que.popleft()
        for dy, dx in ((-1, 0), (0, 1), (1, 0), (0, -1)):
            for k in range(1, K + 1):
                ny, nx = cy + k * dy, cx + k * dx
                if 0 <= ny < H and 0 <= nx < W:
                    if c[ny][nx] == '@':
                        break
                    if cost[ny][nx] <= cost[cy][cx]:
                        break
                    ncost = cost[cy][cx] + 1
                    if ncost < cost[ny][nx]:
                        cost[ny][nx] = ncost
                        que.append((ny, nx))
    print(cost[gy][gx] if cost[gy][gx] != INF else -1)


if __name__ == '__main__':
    solve()