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 queue
class gridMan:
  def __init__(s, L):
    s.L = L
    s.H = len(s.L)
    s.W = len(s.L[0])
  def makeWall(s, x = -2):
    w = len(s.L[0]) + 2
    s.L = [[x] * w] + [[x] + i + [x] for i in s.L] + [[x] * w]
  def dist(s, S): #Sから上下左右に進んで何手かかるかのリスト　および　最大値
    T = [[-1] * s.W for _ in range(s.H)]
    q = queue.Queue()
    q.put([S[0], S[1]])
    T[S[0]][S[1]] = 0
    k = 0
    while not q.empty():
      h, w = q.get()
      k = T[h][w]
      for i, j in [[1, 0], [-1, 0], [0, 1], [0, -1]]:
        hh = h + i
        ww = w + j
        if s.L[hh + 1][ww + 1] >= 0 and T[hh][ww] == -1:
          q.put([hh, ww])
          T[hh][ww] = k + 1
    return T, k

H, W, K = list(map(int, input().split()))
A = [list(input()) for _ in range(H)]

b = "#"
r = "."

for i in range(H):
  for j in range(W):
    if A[i][j] == b:
      A[i][j] = -1
    elif A[i][j] == r:
      A[i][j] = 0
    else:
      A[i][j] = 0
      S = [i, j]

if S[0] == 0 or S[0] == H - 1:
  print(0)
  exit()
if S[1] == 0 or S[1] == W - 1:
  print(0)
  exit()
g = gridMan(A)
g.makeWall()

L, r = g.dist(S)

ans = 10 ** 10
for i in range(H):
  for j in range(W):
    if 0 <= L[i][j] and L[i][j] <= K:
      t = min(i, j, H - i - 1, W - j - 1)
      if t == 0:
        print(1)
        exit()
      t = (t + K - 1) // K
      ans = min(ans, t)

print(ans + 1)