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
input=sys.stdin.readline
sys.setrecursionlimit(10**9)
from collections import deque
from math import ceil

h,w,k=map(int,input().split())
MAP=[]
for i in range(h):
    s=list(input().strip())
    for j,t in enumerate(s):
        if t=='S':
            sx,sy=i,j
    MAP.append(s)
delta=[[1,0],[0,1],[-1,0],[0,-1]]
q=deque()
q.append((sx,sy,k))
dist=float('inf')
Visited=[[False]*w for _ in range(h)]
Visited[sx][sy]=True
while len(q)>0:
    x,y,t=q.popleft()
    dist=min(dist,x,y,h-1-x,w-1-y)
    if dist==0:
        break
    if t>0:
        t-=1
        for dx,dy in delta:
            if MAP[x+dx][y+dy]=='.' and not Visited[x+dx][y+dy]:
                q.append((x+dx,y+dy,t))
                Visited[x+dx][y+dy]=True
print(1+ceil(dist/k))