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 JAVA):

Solution:
import java.util.*;

class Main {

    static int H;
    static int W;
    static int K;
    static char[][] A;
    static int[][] dist;
    static int min;
    static ArrayList<int[]> list;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        H = sc.nextInt();
        W = sc.nextInt();
        K = sc.nextInt();
        A = new char[H][W];
        dist = new int[H][W];
        for (int i=0;i<H;i++) {
            for (int j=0;j<W;j++) {
                dist[i][j] = 19191919;
            }
        }
        min = 19191919;
        list = new ArrayList<int[]>();
        int[] add_1 = {1, 0};int[] add_2 = {-1, 0};int[] add_3 = {0, 1};int[] add_4 = {0, -1};
        list.add(add_1);list.add(add_2);list.add(add_3);list.add(add_4);
        int sy = -1;
        int sx = -1;
        for (int i=0;i<H;i++) {
            String S = sc.next();
            for (int j=0;j<W;j++) {
                A[i][j] = S.charAt(j);
                if (A[i][j]=='S') {
                    A[i][j] = '.';
                    sy = i;
                    sx = j;
                }
            }
        }
        int[] first = {sy, sx, 0};
        ArrayDeque<int[]> q = new ArrayDeque<int[]>();
        q.add(first);
        while (!q.isEmpty()) {
            int[] rem = q.poll();
            int y = rem[0];
            int x = rem[1];
            int k = rem[2];
            if (dist[y][x]<=k) continue;
            dist[y][x] = k;
            min = Math.min(min, y);
            min = Math.min(min, H-1-y);
            min = Math.min(min, x);
            min = Math.min(min, W-1-x);

            if (k==K) continue;

            for (int[] arr : list) {
                if (0<=y+arr[0] && y+arr[0]<H && 0<=x+arr[1] && x+arr[1]<W && A[y+arr[0]][x+arr[1]]=='.') {
                    int[] add = {y+arr[0], x+arr[1], k+1};
                    q.add(add);
                }
            }

        }

        System.out.println((min+K-1)/K+1);
    }
}