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
input = sys.stdin.readline

import queue
class gridMan:
  def __init__(s, L):
    s.L = L
    s.H = len(s.L)
    s.W = len(s.L[0])
  def makeWall(s, x = -2):
    w = len(s.L[0]) + 2
    s.L = [[x] * w] + [[x] + i + [x] for i in s.L] + [[x] * w]
  def dist(s, S): #Sから上下左右に進んで何手かかるかのリスト　および　最大値
    T = [[-1] * s.W for _ in range(s.H)]
    q = queue.Queue()
    q.put([S[0], S[1]])
    T[S[0]][S[1]] = 0
    k = 0
    while not q.empty():
      h, w = q.get()
      p = T[h][w]
      for i, j in [[1, 0], [-1, 0], [0, 1], [0, -1]]:
        for k in range(1, K + 1):
          hh = h + i * k
          ww = w + j * k
          if s.L[hh + 1][ww + 1] >= 0:
            if T[hh][ww] == -1 or T[hh][ww] > p + 1:
              q.put([hh, ww])
              T[hh][ww] = p + 1
            elif T[hh][ww] != p + 1:
              break
          else:
            break
            
    return T, k


H, W, K = list(map(int, input().split()))
xy = list(map(int, input().split()))
c = []
for i in range(H):
  c.append(list(input().replace("\n", "")))

for i in range(H):
  for j in range(W):
    if c[i][j] == ".":
      c[i][j] = 0
    else:
      c[i][j] = -1

g = gridMan(c)
g.makeWall()

L, k = g.dist([xy[0] - 1, xy[1] - 1])

print(L[xy[2] - 1][xy[3] - 1])