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

h,w,k=map(int,input().split())
a=[ [c for c in input()] for _ in range(h)]

s=False
for i in range(h):
    for j in range(w):
        if a[i][j]=="S":
            s=(i,j)
            break
    if s:
        break
min_dis=w*h
dq=collections.deque()
dq.append((0,s[0],s[1]))

moved=[[False for _ in  range(w)] for _ in range(h)]
while dq:
    m,y,x=dq.popleft()
    if moved[y][x]:
        continue
    else:
        moved[y][x]=True
    if m>k:
        continue
    if y==0 or y==h-1 or x==0 or x==w-1:
        print(1)
        exit()
    min_dis=min(min_dis, y, h-1-y, x, w-x-1)
    for dy,dx in ((1,0),(0,1),(-1,0),(0,-1)):
        if 0<=y+dy<h and 0<=x+dx<w and a[y+dy][x+dx] == '.' and not moved[y+dy][x+dx]:
            dq.append((m+1, y+dy, x+dx))
print(1+(min_dis+k-1)//k)