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
from collections import deque as dq
input = sys.stdin.readline
H, W, K = map(int, input().split())
a = []
s = 0
for _ in range(H): a += list(input())[: -1]
for i in range(H * W):
  if a[i] == "S":
    s = i
    break
Q = dq([s])
d = [-1, 0, 1, 0]
dp = [float("inf")] * (H * W)
dp[s] = 0
while len(Q):
  p = Q.popleft()
  for k in range(4):
    q = p + d[k] + d[-1 - k] * W
    if q in range(H * W):
      if a[q] == "#": continue
      if dp[p] + 1 < dp[q]:
        dp[q] = dp[p] + 1
        Q.append(q)
res = float("inf")
for i in range(H * W):
  if dp[i] > K: continue
  n = i // W
  s = H - (i // W) - 1
  e = W - (i % W) - 1
  w = i % W
  res = min(res, -(-min(n, s, e, w) // K))
print(res + 1)