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.io.*;
import java.util.*;

public class Main {
    public static final long mod = (long)1e9+7;
    public static final long INF = Long.MAX_VALUE/2;
    public static final int inf = Integer.MAX_VALUE/2;
    //agc14 c
    static void solve(InputReader in, PrintWriter out){
        int h = in.ni(), w = in.ni(), k = in.ni();
        char[][] map = new char[h][w];
        for (int i = 0; i < h; i++) {
            map[i] = in.ns().toCharArray();
        }
        int sx = 0, sy = 0;
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                if(map[i][j]=='S'){
                    sx = i;
                    sy = j;
                }
            }
        }
        int[] dx = new int[]{0,1,0,-1};
        int[] dy = new int[]{1,0,-1,0};
        ArrayDeque<Pair> que = new ArrayDeque<Pair>();
        que.addFirst(new Pair(sx, sy));
        int[][] dist = new int[h][w];
        for (int i = 0; i < h; i++) Arrays.fill(dist[i], inf);
        dist[sx][sy] = 0;
        while(!que.isEmpty()){
            Pair p = que.pollLast();
            for (int i = 0; i < 4; i++) {
                int x = p.x+dx[i], y = p.y+dy[i];
                if(x>=0&&x<h&&y>=0&&y<w&&map[x][y]=='.'){
                    if(dist[x][y] == inf){
                        dist[x][y] = dist[p.x][p.y]+1;
                        if(dist[x][y]<k) que.addFirst(new Pair(x, y));
                    }
                }
            }

        }
        int ans = inf;
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                if(dist[i][j]<=k){
                    int len1 = Math.min((h-i-2+k)/k, (i+k-1)/k);
                    int len2 = Math.min((w-j-2+k)/k, (j+k-1)/k);
                    ans = Math.min(ans, Math.min(len1, len2)+1);
                }
            }
        }
        out.println(ans);
    }
    public static class Pair{
        int x; int y;
        public Pair(int x, int y){
            this.x = x;
            this.y = y;
        }
    }

    public static void main(String[] args){
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        solve(in, out);
        out.close();
    }
    public static class InputReader{
        private BufferedReader br;
        private StringTokenizer st;
        public InputReader(InputStream is){
            br = new BufferedReader(new InputStreamReader(is));
            st = null;
        }
        public String ns(){
            if(st == null || !st.hasMoreTokens()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (Exception e){
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }
        public int ni(){
            return Integer.parseInt(ns());
        }
        public long nl(){
            return Long.parseLong(ns());
        }
        public double nd(){
            return Double.parseDouble(ns());
        }
        public char nc(){
            return ns().toCharArray()[0];
        }
        public int[] ni(int n){
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }
        public long[] nl(int n){
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nl();
            }
            return a;
        }
        public double[] nd(int n){
            double[] a = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nd();
            }
            return a;
        }
    }
}