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 heappush, heappop
import sys
input = sys.stdin.readline

H, W, K = map(int, input().split())
x1, y1, x2, y2 = map(int, input().split())
c = [[i == '.' for i in input()] for _ in range(H)]

x1, y1, x2, y2 = x1 - 1, y1 - 1, x2 - 1, y2 - 1
INF = 1 << 60
dist = [INF] * (H * W * 2)

def pos(x, y, m) :
  return (x * W + y) * 2 + m
dist[pos(x1, y1, 0)] = dist[pos(x1, y1, 1)] = 0

q = [(0, pos(x1, y1, 0)), (0, pos(x1, y1, 1))]
while q :
  ccost, cpos = heappop(q)
  if ccost > dist[cpos] : continue
  cx = cpos // 2 // W
  cy = cpos // 2 % W
  cmode = cpos % 2
  dir = [
    [(-1, 0), (1, 0)],
    [(0, -1), (0, 1)]
  ]
  for dx, dy in dir[cmode] :
    nx, ny = cx + dx, cy + dy
    ncost = ccost + 1
    if 0 <= nx < H and 0 <= ny < W and c[nx][ny] and ncost < dist[pos(nx, ny, cmode)] :
      heappush(q, (ncost, pos(nx, ny, cmode)))
      dist[pos(nx, ny, cmode)] = ncost
      
  ncost = (ccost + K - 1) // K * K
  if ncost < dist[pos(cx, cy, cmode ^ 1)] :
    dist[pos(cx, cy, cmode ^ 1)] = ncost
    heappush(q, (ncost, pos(cx, cy, cmode ^ 1)))

ans = min(dist[pos(x2, y2, 0)], dist[pos(x2, y2, 1)])
if ans == INF :
  print(-1)
else :
  print((ans + K - 1) // K)