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
from collections import deque
readline = sys.stdin.readline

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

G = [[2]*(W+2)]

st = (None, None)
for h in range(H):
    g = readline().strip()
    if 'S' in g:
        st = (1+h, 1+g.index('S'))
    
    G.append([2] + [1 if s == '#' else 0 for s in g] + [2])

G.append([2]*(W+2))

DIREC = [(0, -1), (0, 1), (1, 0), (-1, 0)]

Q = deque([st])
INF = 10**9+7
dist = [[INF]*(W+2) for _ in range(H+2)]
for h, w in Q:
    dist[h][w] = 0


Q2 = deque([st])
ans = INF
while Q:
    nh, nw = Q.pop()
    for dh, dw in DIREC:
        fh, fw = nh+dh, nw+dw
        if G[fh][fw]:
            continue
        if dist[fh][fw] > 1 + dist[nh][nw]:
            dist[fh][fw] = 1 + dist[nh][nw]
            if dist[fh][fw] <= K:
                Q2.append((fh, fw))
                if fh == 1 or fh == H or fw == 1 or fw == W:
                    ans = 1
            Q.appendleft((fh, fw))

if ans == INF:
    dist = [[INF]*(W+2) for _ in range(H+2)]
    for h, w in Q2:
        dist[h][w] = 0
    while Q2:
        nh, nw = Q2.pop()
        for dh, dw in DIREC:
            fh, fw = nh+dh, nw+dw
            if G[fh][fw] == 2:
                continue
            if dist[fh][fw] > 1 + dist[nh][nw]:
                dist[fh][fw] = 1 + dist[nh][nw]
                if fh == 1 or fh == H or fw == 1 or fw == W:
                    ans = min(ans, 2+(dist[fh][fw]-1)//K)
                Q2.appendleft((fh, fw))

print(ans)