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
sys.setrecursionlimit(500000) #これがないと再帰の回数オーバーでエラー出る。
from collections import deque
INF = float("inf")
H,W,K = map(int,input().split())
Room = []
for i in range(H):
  temp = str(input())
  temp = list(temp)
  for j in range(W):
    if temp[j] == "S":
      sx = i;sy =j
  Room.append(temp)
#print(sx,sy)
d = [(1,0),(-1,0),(0,1),(0,-1)]

R = [[INF]*W for _ in range(H)]
R[sx][sy] = 0
reach = set([])
reach.add((sx,sy))
Q = deque([[sx,sy]])
while Q:
  x,y = Q.popleft()
  if x==0 or x==H-1 or y==0 or y==W-1:
    print(1)
    exit()
  if R[x][y] == K:
    #L.add((x,y))
    #if stp == K:
    continue
  #stp +=1
  for i in range(4):
    nx = x+d[i][0]
    ny = y+d[i][1]
    #print(nx,ny)
    if nx<0 or nx>=H or ny<0 or ny>= W or Room[nx][ny] == "#" or R[nx][ny] != INF:
      continue
    reach.add((nx,ny))
    R[nx][ny] = R[x][y] + 1
    Q.append([nx, ny])
    #print(Q)

ans = INF

for t in reach:
  x,y = t[0],t[1]
  nokori = min(x,H-1-x,y,W-1-y)
  step = (nokori+K-1)//K + 1 #1は最初のステップ
  ans = min(ans,step)
print(ans)