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:
from collections import deque

def main():
    H, W, K = map(int, input().split())
    A = [input() for _ in range(H)]
    s = None
    for i in range(H):
        for j in range(W):
            if A[i][j] == "S":
                s = (i, j)
    q = deque()
    q.append((s[0], s[1], K))
    directions = [(0, 1), (1, 0), (0, -1), (-1, 0)]
    visited = [[False] * W for _ in range(H)]
    visited[s[0]][s[1]] = True
    dst = float("inf")
    while(len(q)):
        i, j, m = q.popleft()
        dst = min(dst, min([i, j, H-1-i, W-1-j]))
        if m == 0:
            continue
        for d in directions:
            ni = i + d[0]
            nj = j + d[1]
            if 0 <= ni < H and 0 <= nj < W:
                if A[ni][nj] == "." and not visited[ni][nj]:
                    q.append((ni, nj, m-1))
                    visited[ni][nj] = True
    ans = 1 - (-dst//K)
    print(ans)


if __name__ == "__main__":
    main()