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
# リストの両端の要素に対する編集が必要
# 同一方向に進むときは移動回数が増えないためリストのの先頭に挿入
# この仕組みを実装するためdequeを読み込み

H, W, K = map(int, input().split())
# HとWとKの値それぞれを取得

x1, y1, x2, y2 = map(int, input().split())
x1 -= 1
y1 -= 1
x2 -= 1
y2 -= 1
# リストの先頭要素は0番目として数えられる
# 座標のそれぞれの値から1を引いて取得

grid = [input() for _ in range(H)]
# グリッド部分をH行にわたって取得

INF = float('inf')
path = [[[(INF, INF)] * 4 for _ in range(W)] for _ in range(H)]
# 無限大の浮動小数点を管理

D = [(-1, 0), (0, 1), (1, 0), (0, -1)]
# 進行方向を座標で管理

q = deque()
for d in range(4):
	path[x1][y1][d] = (1, 0)
	# スタート地点を(1, 0)に設定
	q.append((x1, y1, d, 1, 0))
	# (x, y, 進行方向, 移動回数, 進行済マス数)を要素に追加

while q:
	x, y, d, c, k = q.popleft()
	#要素の削除
	
	# nx, ny: 次の座標
	# nd: 次の進行方向
	# nc: 次の移動回数
	# nk: 次の進行済マス数
	
	for nd in range(4):
		if nd == d:
			dx, dy = D[nd]
			nk = 1 if k == K else k + 1
			nc = c + 1 if k == K else c
		else:
			dx, dy = 0, 0
			nk = 0
			nc = c + 1
		nx = x + dx; ny = y + dy
		if 0 <= nx < H and 0 <= ny < W and grid[nx][ny] == '.' and path[nx][ny][nd] > (nc, nk):
			path[nx][ny][nd] = (nc), (nk)
			if nc == c:
				q.appendleft((nx, ny, nd, nc, nk))
			else:
				q.append((nx, ny, nd, nc, nk))
				
# コストの算出
ans = INF
for d in range(4):
	ans = min(ans, path[x2][y2][d][0])
ans = -1 if ans == INF else ans

print(ans)