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:
def solve():
    dxys = [(-1,0), (1,0), (0,-1), (0,1)]

    H, W, K = map(int, input().split())
    Ass = ['#'*(W+2)] + ['#'+input()+'#' for _ in range(H)] + ['#'*(W+2)]

    def find2D(Sss, ch):
        for x, Ss in enumerate(Sss):
            y = Ss.find(ch)
            if y != -1:
                return (x, y)
        return (-1, -1)

    xS, yS = find2D(Ass, 'S')

    usedss = [[False]*(W+2) for _ in range(H+2)]
    usedss[xS][yS] = True
    vs = set([(xS, yS)])
    for _ in range(K):
        v2s = set()
        for x, y in vs:
            for dx, dy in dxys:
                x2, y2 = x+dx, y+dy
                if not usedss[x2][y2] and Ass[x2][y2] == '.':
                    usedss[x2][y2] = True
                    v2s.add((x2, y2))
        vs = v2s

    ans = 10**5
    for x in range(H):
        for y in range(W):
            if usedss[x+1][y+1]:
                dist = min(x, H-1-x, y, W-1-y)
                ans = min(ans, -(-dist//K)+1)
    print(ans)

solve()