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 math
import copy
temp=input().split()
H=int(temp[0])
W=int(temp[1])
K=int(temp[2])
A=[[i for i in input()] for j in range(H)]
place=[[K+2 for j in range(W)] for i in range(H)]
ans=0

si=0
sj=0
for i in range(H):
	for j in range(W):
		if A[i][j]=="S":
			si=i
			sj=j
			A[i][j]="."
			break
	else:
		continue
	break

now=[[si,sj]]
place[si][sj]=0
next=[]
for i in range(K):
	for room in now:
		if A[room[0]-1][room[1]]=="." and place[room[0]-1][room[1]]==K+2:
			place[room[0]-1][room[1]]=i
			next.append([room[0]-1,room[1]])
			if room[0]-1==0:
				ans=-1
		if A[room[0]+1][room[1]]=="." and place[room[0]+1][room[1]]==K+2:
			place[room[0]+1][room[1]]=i
			next.append([room[0]+1,room[1]])
			if room[0]+1==H-1:
				ans=-1
		if A[room[0]][room[1]-1]=="." and place[room[0]][room[1]-1]==K+2:
			place[room[0]][room[1]-1]=i
			next.append([room[0],room[1]-1])
			if room[1]-1==0:
				ans=-1
		if A[room[0]][room[1]+1]=="." and place[room[0]][room[1]+1]==K+2:
			place[room[0]][room[1]+1]=i
			next.append([room[0],room[1]+1])
			if room[1]+1==W-1:
				ans=-1
	if ans==-1:
		break
	now=copy.deepcopy(next)
	next=[]
		
little=H+W
goodi=-1
goodj=-1
for i in range(H):
	for j in range(W):
		if place[i][j]!=K+2:
			little=min(little,i,j,H-1-i,W-1-j)
			goodi=i
			goodj=j
print(math.ceil(little/K)+1)