Closed Rooms

Takahashi is locked within a building.

This building consists of H×W rooms, arranged in H rows and W columns. We will denote the room at the i-th row and j-th column as (i,j). The state of this room is represented by a character A_{i,j}. If A_{i,j}= #, the room is locked and cannot be entered; if A_{i,j}= ., the room is not locked and can be freely entered. Takahashi is currently at the room where A_{i,j}= S, which can also be freely entered.

Each room in the 1-st row, 1-st column, H-th row or W-th column, has an exit. Each of the other rooms (i,j) is connected to four rooms: (i-1,j), (i+1,j), (i,j-1) and (i,j+1).

Takahashi will use his magic to get out of the building. In one cast, he can do the following:

• Move to an adjacent room at most K times, possibly zero. Here, locked rooms cannot be entered.
• Then, select and unlock at most K locked rooms, possibly zero. Those rooms will remain unlocked from then on.

His objective is to reach a room with an exit. Find the minimum necessary number of casts to do so.

It is guaranteed that Takahashi is initially at a room without an exit.

Constraints

• 3 ≤ H ≤ 800
• 3 ≤ W ≤ 800
• 1 ≤ K ≤ H×W
• Each A_{i,j} is # , . or S.
• There uniquely exists (i,j) such that A_{i,j}= S, and it satisfies 2 ≤ i ≤ H-1 and 2 ≤ j ≤ W-1.

Input

Input is given from Standard Input in the following format:

H W K A_{1,1}A_{1,2}...A_{1,W} : A_{H,1}A_{H,2}...A_{H,W}

Output

Print the minimum necessary number of casts.

Examples

Input

3 3 3 #.# #S.

Output

1

Input

3 3 3 .# S.

Output

1

Input

3 3 3

S#

Output

2

Input

7 7 2

...## S### .#.## .###

Output

2

inputFormat

Input

Input is given from Standard Input in the following format:

H W K A_{1,1}A_{1,2}...A_{1,W} : A_{H,1}A_{H,2}...A_{H,W}

outputFormat

Output

Print the minimum necessary number of casts.

Examples

Input

3 3 3 #.# #S.

Output

1

Input

3 3 3 .# S.

Output

1

Input

3 3 3

S#

Output

2

Input

7 7 2

...## S### .#.## .###

Output

2

样例

3 3 3
#.#
#S.
###

1