Pond Skater

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

inputFormat

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}

outputFormat

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

样例

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

5