Problem: 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

Solution (in PYTHON3):

Solution:
import sys
def main():
    input = sys.stdin.readline
    H,W,K=map(int, input().split())
    A=[list(input()) for _ in range(H)]

    from collections import deque
    q=deque()
    for i in range(H):
        for j in range(W):
            if A[i][j]=='S':
                q.append((i,j,0))
                A[i][j]='#'

    ans=10**9
    while q:
        i,j,d = q.popleft()
        if i==0 or i==H-1 or j==0 or j==W-1:
            print(1)
            exit()
        ans = min(ans, (min(i,j,H-1-i,W-1-j) + K-1) // K + 1)
        if d==K: continue
        for di,dj in ((-1,0),(1,0),(0,-1),(0,1)):
            ni,nj=i+di,j+dj
            if A[ni][nj]!='#':
                q.append((ni,nj,d+1))
                A[ni][nj]='#'
    print(ans)

if __name__ == '__main__':
    main()