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
input = sys.stdin.readline


def main():
    H, W, K = map(int, input().split())
    state = [list(input()) for _ in range(H)]


    q = []
    checked = [[False]*W for _ in range(H)]
    for h in range(H):
        for w in range(W):
            if state[h][w] == "S":
                q.append((h, w))
                checked[h][w] = True

    goal = False
    for _ in range(K):
        qq = []
        for h, w in q:
            if h == 0 or h == H-1 or w == 0 or w == W-1:
                goal = True
                break
            nexts = [(h, w-1), (h, w+1), (h-1, w), (h+1, w)]
            for nh, nw in nexts:
                if state[nh][nw] == "." and not checked[nh][nw]:
                    checked[nh][nw] = True
                    qq.append((nh, nw))
        q = qq
    if goal:
        print(1)
    else:
        ans = 10**14
        for h in range(H):
            for w in range(W):
                if checked[h][w]:
                    d1 = min(h, H-1-h)
                    d2 = min(w, W-1-w)
                    D = min(d1//K + min(d1%K, 1), d2//K + min(d2%K, 1))
                    ans = min(D+1, ans)
        print(ans)


if __name__ == "__main__":
    main()