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 collections

def solve():
  def calc(x,y):
    cnt1=(x+k-1)//k
    cnt2=(w-1-x+k-1)//k
    cnt3=(y+k-1)//k
    cnt4=(h-1-y+k-1)//k
    return min(cnt1,cnt2,cnt3,cnt4)

  h,w,k=map(int,input().split())
  boards=[tuple(input()) for _ in range(h)]
  for i in range(h):
    for j in range(w):
      if boards[i][j]=='S':
        sx=j
        sy=i
        break
  q=collections.deque()
  checked=[[0]*w for _ in range(h)]
  checked[sy][sx]=1
  q.append((sx,sy,0))
  ans=1+calc(sx,sy)
  while 1:
    if len(q)==0:
      break
    tx,ty,cnt=q.popleft()
    if cnt==k+1:
      break
    ans=min(ans,1+calc(tx,ty))
    if tx!=0 and boards[ty][tx-1]!='#' and checked[ty][tx-1]==0:
      checked[ty][tx-1]=1
      q.append((tx-1,ty,cnt+1))
    if tx!=w-1 and boards[ty][tx+1]!='#' and checked[ty][tx+1]==0:
      checked[ty][tx+1]=1
      q.append((tx+1,ty,cnt+1))
    if ty!=0 and boards[ty-1][tx]!='#' and checked[ty-1][tx]==0:
      checked[ty-1][tx]=1
      q.append((tx,ty-1,cnt+1))
    if ty!=h-1 and boards[ty+1][tx]!='#' and checked[ty+1][tx]==0:
      checked[ty+1][tx]=1
      q.append((tx,ty+1,cnt+1))
  print(ans)
solve()