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

def updiv(a,b):
    if a % b == 0:
        return a // b
    else:
        return a // b + 1

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

A = []

for i in range(H):

    a = list(input())
    A.append(a)

q = deque([])

#print (A)

for i in range(H):

    for j in range(W):

        if A[i][j] == "S":
            q.append([i,j])
            A[i][j] = 0

while len(q) > 0:

    now = q.popleft()
    ni = now[0]
    nj = now[1]

    if A[ni][nj] < K:
        if ni-1 >= 0 and A[ni-1][nj] != "#":
            if A[ni-1][nj] == "." or A[ni][nj]+1 < A[ni-1][nj]:
                A[ni-1][nj] = A[ni][nj] + 1
                q.append([ni-1,nj])

        if ni+1 < H and A[ni+1][nj] != "#":
            if A[ni+1][nj] == "." or A[ni][nj]+1 < A[ni+1][nj]:
                A[ni+1][nj] = A[ni][nj] + 1
                q.append([ni+1,nj])

        if nj-1 >= 0 and A[ni][nj-1] != "#":
            if A[ni][nj-1] == "." or A[ni][nj]+1 < A[ni][nj-1]:
                A[ni][nj-1] = A[ni][nj] + 1
                q.append([ni,nj-1])

        if nj+1 < W and A[ni][nj+1] != "#":
            if A[ni][nj+1] == "." or A[ni][nj]+1 < A[ni][nj+1]:
                A[ni][nj+1] = A[ni][nj] + 1
                q.append([ni,nj+1])

ans = float("inf")
#print (A)

for i in range(H):

    for j in range(W):

        if A[i][j] not in [".","#"]:
            ans = min(ans , 1 + updiv(i,K) , 1 + updiv(j,K) , 1 + updiv(H-i-1,K), 1 + updiv(W-j-1, K))

print (ans)