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 main():
    h, w, k = map(int, input().split())
    grid = ["."*(w+2)]+["."+input()+"." for _ in [0]*h]+["."*(w+2)]
    visit = [[False]*(w+2) for _ in [0]*(h+2)]
    for i in range(h+2):
        for j in range(w+2):
            if grid[i][j] == "S":
                start = (i, j)
                break
    visit[start[0]][start[1]] = True
    q = [start]
    for i in range(k):
        q2 = []
        while q:
            x, y = q.pop()
            if x-1 >= 0:
                if grid[x-1][y] == "." and visit[x-1][y] is False:
                    q2.append((x-1, y))
                    visit[x-1][y] = True
            if x+1 <= h+1:
                if grid[x+1][y] == "." and visit[x+1][y] is False:
                    q2.append((x+1, y))
                    visit[x+1][y] = True
            if y-1 >= 0:
                if grid[x][y-1] == "." and visit[x][y-1] is False:
                    q2.append((x, y-1))
                    visit[x][y-1] = True
            if y+1 <= w+1:
                if grid[x][y+1] == "." and visit[x][y+1] is False:
                    q2.append((x, y+1))
                    visit[x][y+1] = True
        q = q2
    dist = 10**9
    for i in range(h+2):
        for j in range(w+2):
            if visit[i][j]:
                dist = min([dist, i, h+1-i, j, w+1-j])
    print((max(dist-1, 0)-1)//k+2)


main()