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:
H, W, K = list(map(int, input().split()))
MAP = []
for i in range(H):
	MAP.append(list(input()))
for i in range(H):
	for j in range(W):
		if MAP[i][j] == "S":
			h = i
			w = j
			MAP[i][j] = ","
			break
		else:
			pass
length = min([h, w, H - h - 1, W - w - 1])
abl = [[h, w]]
for j in range(K):
	ln = len(abl)
	abll = []
	for i in range(ln):
		if MAP[abl[i][0] + 1][abl[i][1]] == ".":
			if abl[i][0] + 1 == H - 1:
				length = 0
				break
				break
			else:
				if H - abl[i][0] - 2 < length:
					length = H - abl[i][0] - 2
				else:
					pass
				abll.append([abl[i][0] + 1, abl[i][1]])
				MAP[abl[i][0] + 1][abl[i][1]] = ","
		else:
			pass

		if MAP[abl[i][0] - 1][abl[i][1]] == ".":
			if abl[i][0] - 1 == 0:
				length = 0
				break
				break
			else:
				if abl[i][0] - 1 < length:
					length = abl[i][0] - 1
				else:
					pass
				abll.append([abl[i][0] - 1, abl[i][1]])
				MAP[abl[i][0] - 1][abl[i][1]] = ","
		else:
			pass

		if MAP[abl[i][0]][abl[i][1] + 1] == ".":
			if abl[i][1] + 1 == W - 1:
				length = 0
				break
				break
			else:
				if W - abl[i][1] - 2 < length:
					length = W - abl[i][1] - 2
				else:
					pass
				abll.append([abl[i][0], abl[i][1] + 1])
				MAP[abl[i][0]][abl[i][1] + 1] = ","

		if MAP[abl[i][0]][abl[i][1] - 1] == ".":
			if abl[i][1] + 1 == 0:
				length = 0
				break
				break
			else:
				if abl[i][1] - 1 < length:
					length = abl[i][1] - 1
				else:
					pass
				abll.append([abl[i][0], abl[i][1] - 1])
				MAP[abl[i][0]][abl[i][1] - 1] = ","
	abl = abll
if length % K == 0:
	print(int(length // K) + 1)
else:
	print(int(length // K) + 2)