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
import sys
input = sys.stdin.readline

H, W, K = map(int, input().split())
A = [input().rstrip() for _ in range(H)]
si = sj = -1
for i in range(H):
    for j in range(W):
        if A[i][j] == 'S':
            si, sj = i, j
            break
    if si != -1:
        break
# ans = (min(si, H - si - 1, sj, W - sj - 1) + K - 1) // K
queue = deque([(si, sj)])
INF = 10**18
dist = [[INF] * W for _ in range(H)]
dist[si][sj] = 0
ans = INF
while queue:
    i, j = queue.popleft()
    ans = min(ans, 1 + (min(i, H - i - 1, j, W - j - 1) + K - 1) // K)
    if dist[i][j] == K:
        continue
    for di, dj in [(1, 0), (0, 1), (-1, 0), (0, -1)]:
        ni, nj = i + di, j + dj
        if 0 <= ni < H and 0 <= nj < W and A[ni][nj] == '.' and dist[ni][nj] == INF:
            dist[ni][nj] = dist[i][j] + 1
            queue.append((ni, nj))
print(ans)