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

H, W, K = map(int, input().split())

move = [(1, 0), (-1, 0), (0, 1), (0, -1)]

G = [list(input()) for _ in range(H)]
check = [[-1] * (W) for _ in range(H)]

que = deque()

flag = False
for h in range(H):
    for w in range(W):
        if G[h][w] == 'S':
            que.append((h, w))
            flag = True
            break
    if flag:
        break

x_min = h
x_max = h

y_min = w
y_max = w

check[h][w] = 0
while que:
    tmp = que.popleft()
    
    x = tmp[0]
    y = tmp[1]
    
    now_ = check[x][y]
    if now_ == K:
        continue

    for dx, dy in move:
        nx = x + dx
        ny = y + dy
        if not (0 <= nx < H and 0 <= ny < W):
            continue
        if G[nx][ny] == '#':
            continue
        if check[nx][ny] == -1:
            check[nx][ny] = now_ + 1
            que.append((nx, ny))
            
            x_min = min(x_min, nx)
            x_max = max(x_max, nx)

            y_min = min(y_min, ny)
            y_max = max(y_max, ny)

ans = 10 ** 18
ans = min(ans, (x_min + K - 1) // K + 1)
ans = min(ans, (H - x_max - 1 + K - 1) // K + 1)
ans = min(ans, (y_min + K - 1) // K + 1)
ans = min(ans, (W - y_max - 1 + K - 1) // K + 1)

print (ans)