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

readline = sys.stdin.readline
readall = sys.stdin.read
ns = lambda: readline().rstrip()
ni = lambda: int(readline().rstrip())
nm = lambda: map(int, readline().split())
nl = lambda: list(map(int, readline().split()))


def solve():
    h, w, k = nm()
    sy, sx, gy, gx = nm()
    d = [(0, 1), (1, 0), (-1, 0), (0, -1)]
    sx -= 1; sy -= 1
    gx -= 1; gy -= 1
    C = [ns() for _ in range(h)]
    G = [[10**7]*w for _ in range(h)]
    G[sy][sx] = 0
    q = deque([(sy, sx)])
    while q:
        y, x = q.popleft()
        for i in range(4):
            dy, dx = d[i]
            ny, nx = y, x
            for _ in range(k):
                ny += dy; nx += dx
                if ny < 0 or h <= ny or nx < 0 or w <= nx:
                    break
                if C[ny][nx] == '@' or G[ny][nx] <= G[y][x]:
                    break
                if G[ny][nx] > G[y][x] + 1:
                    G[ny][nx] = G[y][x] + 1
                    q.append((ny, nx))
                    if ny == gy and nx == gx:
                        print(G[y][x] + 1)
                        return
    print(-1)
    return

solve()