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())
sh, sw, gh, gw = map(int, input().split())
sh, sw, gh, gw = sh - 1, sw - 1, gh - 1, gw - 1
G = [list(input()) for _ in range(H)]
INF = 10 ** 9


D = [[INF] * W for _ in range(H)]
D[sh][sw] = 0
directions = [(0, 1), (0, -1), (1, 0), (-1, 0)]
que = deque([(sh, sw)])

while que:
    nh, nw = que.pop()
    for dh, dw in directions:
        for k in range(1, K + 1):
            nx_h, nx_w = nh + k * dh, nw + k * dw
            if not (0 <= nx_h < H and 0 <= nx_w < W):
                break

            if G[nx_h][nx_w] == '@':
                break

            if D[nx_h][nx_w] < D[nh][nw] + 1:
                break

            if D[nx_h][nx_w] > D[nh][nw] + 1:
                D[nx_h][nx_w] = D[nh][nw] + 1
                que.appendleft((nx_h, nx_w))

print(D[gh][gw] if D[gh][gw] != INF else -1)