Problem Statement

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.

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.

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.

Sample Input 1

3 5 2
3 2 3 4
.....
.@..@
..@..

Sample Output 1

5

Initially, Snuke is at the square (3,2).
He can reach the square (3, 4) by making five strokes as follows:

• From (3, 2), go west one square to (3, 1).

• From (3, 1), go north two squares to (1, 1).

• From (1, 1), go east two squares to (1, 3).

• From (1, 3), go east one square to (1, 4).

• From (1, 4), go south two squares to (3, 4).

Sample Input 2

1 6 4
1 1 1 6
......

Sample Output 2

2

Sample Input 3

3 3 1
2 1 2 3
.@.
.@.
.@.

Sample Output 3

-1

见题面 Input 部分

见题面 Output 部分