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,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools

sys.setrecursionlimit(10**7)
inf = 10**20
mod = 10**9 + 7

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()


def main():
    h,w,k = LI()
    a = []
    st = None
    for i in range(h):
        s = S()
        if 'S' in s:
            st = [i, s.index('S')]
        a.append([c=='#' for c in s])

    def ns(k):
        i,j = k
        r = []
        if i < h-1:
            r.append((i+1,j))
        if j < w-1:
            r.append((i,j+1))
        if i > 0:
            r.append((i-1,j))
        if j > 0:
            r.append((i,j-1))
        return r


    def search(ss,tk):
        d = collections.defaultdict(lambda: inf)
        q = []
        for s in ss:
            d[s] = 0
            heapq.heappush(q, (0, s))
        v = collections.defaultdict(bool)
        while len(q):
            k, u = heapq.heappop(q)
            if k >= tk:
                break
            if v[u]:
                continue
            v[u] = True

            for nu in ns(u):
                if v[nu] or a[nu[0]][nu[1]]:
                    continue
                vd = k + 1
                if d[nu] > vd:
                    d[nu] = vd
                    if nu[0] == 0 or nu[1] == 0 or nu[0] == h-1 or nu[1] == w-1:
                        return d
                    heapq.heappush(q, (vd, nu))

        return d

    d = search([tuple(st)],k)
    r = inf
    hs = []
    ws = []
    for g in d.keys():
        if 0 < g[0] < h-1 and 0 < g[1] < w-1:
            hs.append(g[0])
            ws.append(g[1])
            continue
        return 1

    return (min(min(hs),min(ws),h-max(hs)-1,w-max(ws)-1) + k - 1) // k + 1

print(main())