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:
def ii():return int(input())
def iim():return map(int,input().split())
def iil():return list(map(int,input().split()))
from collections import deque


def bfs(xg,yg):
    queue = deque([(xs,ys,0)])
    while queue:
        x,y,dep = queue.popleft()
        l = []
        for xx,yy in [(1,0),(0,1),(-1,0),(0,-1)]:
            for i in range(1,k+1):
                nx,ny = x+xx*i,y+yy*i
                if cord[ny][nx] == '.':
                    l.append((nx,ny))
                elif type(cord[ny][nx]) != int or cord[ny][nx] < dep+1:
                    break
        for nx, ny in l:
            if cord[ny][nx] == '.':
                cord[ny][nx] = dep+1
                if (nx,ny) == (xg,yg):
                    return dep+1
                else:
                    queue.append((nx,ny,dep+1))
    return -1

h,w,k = iim()
ys,xs,yg,xg = iim()

cord = [['@']*(w+2)]
for i in range(h):
    cord.append(['@']+list(input())+['@'])
cord.append(['@']*(w+2))
cord[ys][xs] = '#'

print(bfs(xg,yg))