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 numpy as np
import queue
from collections import deque,defaultdict
import heapq as hpq
from sys import stdin,setrecursionlimit
#from scipy.sparse.csgraph import dijkstra
#from scipy.sparse import csr_matrix
ipt = stdin.readline
setrecursionlimit(10**7)

def main():
    h,w,k = map(int,ipt().split())
    a = [input() for _ in range(h)]
    for i,ai in enumerate(a):
        if "S" in ai:
            si = i
            sj = ai.find("S")
            break
    q = queue.Queue()
    t = [[10**10]*w for _ in [0]*h]
    dir = [(-1,0),(1,0),(0,-1),(0,1)]
    t[si][sj] = 0
    q.put((si,sj))
    g1 = [(si,sj)]
    while not q.empty():
        qi,qj = q.get()
        for di,dj in dir:
            if 0 <= qi+di <= h-1 and 0 <= qj+dj <= w-1 and a[qi+di][qj+dj] == ".":
                if t[qi+di][qj+dj] > t[qi][qj] + 1:
                    t[qi+di][qj+dj] = t[qi][qj] + 1
                    g1.append((qi+di,qj+dj))
                    if t[qi][qj] != k-1:
                        q.put((qi+di,qj+dj))

    mi = 10**4
    for i,j in g1:
        if mi > (i+k-1)//k+1:
            mi = (i+k-1)//k+1
        if mi > (j+k-1)//k+1:
            mi = (j+k-1)//k+1
        if mi > (h-1-i+k-1)//k+1:
            mi = (h-1-i+k-1)//k+1
        if mi > (w-1-j+k-1)//k+1:
            mi = (w-1-j+k-1)//k+1
    print(mi)
    return

if __name__ == '__main__':
    main()