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 heapq import heappop, heappush
import sys
input = sys.stdin.readline
H, W, K = map(int, input().split())
x1, y1, x2, y2 = map(lambda x: int(x)-1, input().split())
S = [input()[:-1] for _ in [0]*H]

def geth(x, y, z):
    return (x*W+y)*4+z

def push(x, y, z, d):
    h = geth(x, y, z)
    if D[h] <= d:
        return
    D[h] = d
    heappush(q, (d, h))

INF = 10**10
MAX = H*W*4
D = [INF]*MAX
dirs = [(-1, 0), (0, -1), (1, 0), (0, 1)]

q = []
for z in range(4):
    heappush(q, (0, geth(x1, y1, z)))

while q:
    d, h = heappop(q)
    z = h % 4
    x, y = divmod((h//4), W)

    if d > D[h]:
        continue
    D[h] = d

    for _z, (dx, dy) in enumerate(dirs):
        if _z == z:
            _x, _y = x+dx, y+dy
            if 0 <= _x < H and 0 <= _y < W and S[_x][_y] == '.':
                push(_x, _y, z, d+1)
        else:
            _h = geth(x, y, _z)
            _d = (d+K-1)//K*K
            push(x, y, _z, _d)

g = geth(x2, y2, 0)
ans = min(D[g:g+4])
if ans == INF:
    print(-1)
else:
    ans = (ans-1+K)//K
    print(ans)