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:
from collections import deque

H, W, K = map(int, input().split())

chart = [list(input()) for _ in range(H)]

start = (-1, -1)
for h in range(H):
    for w in range(W):
        if chart[h][w] == 'S':
            start = (h, w)
            chart[h][w] = '.'

minDist  = [[float('inf')] * W for _ in range(H)]
que = deque([(start[0], start[1], 0)])
while que:
    nh, nw, dist = que.popleft()

    if minDist[nh][nw] <= dist:
        continue

    minDist[nh][nw] = dist
    if dist == K:
        continue

    for toH in [nh - 1, nh + 1]:
        if toH < 0 or toH >= H:
            continue
        if chart[toH][nw] == '.':
            que.append((toH, nw, dist + 1))
    for toW in [nw - 1, nw + 1]:
        if toW < 0 or toW >= W:
            continue
        if chart[nh][toW] == '.':
            que.append((nh, toW, dist + 1))

ans = float('inf')
for h in range(H):
    for w in range(W):
        if minDist[h][w] == float('inf'):
            continue
        d = min(h, w, H - h - 1, W - w - 1)
        if d == 0:
            ans = min(ans, 1)
        else:
            ans = min(ans, -(-d // K) + 1)

print(ans)