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
def input():
	return sys.stdin.readline()[:-1]
from collections import deque
H, W, K = map(int, input().split())
sh, sw, gh, gw = map(int, input().split())
c = ["@" * (W+2)] + ["@" + input() + "@" for _ in range(H)] + ["@" * (W+2)]
INF = 10**6+5
dist = [[INF for _ in range(W+2)] for _ in range(H+2)]
dist[sh][sw] = 0
q = deque()
q.append(sh*(W+2)+sw)
DI = [1, 0, -1, 0]
DJ = [0, 1, 0, -1]
while q:
	l = q.popleft()
	i, j = l//(W+2), l%(W+2)
	for di, dj in zip(DI, DJ):
		for k in range(1, K+1):
			ii, jj = i+di*k, j+dj*k
			if c[ii][jj] == "@":
				break
			if dist[ii][jj] <= dist[i][j]:
				break
			if dist[ii][jj] > dist[i][j] + 1:
				dist[ii][jj] = dist[i][j] + 1
				if ii == gh and jj == gw:
					print(dist[ii][jj])
					sys.exit()
				q.append(ii*(W+2) + jj)
print(-1)