Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3 3 3
#.#
#S.
###

Sample Output 1

1

Takahashi can move to room (1,2) in one cast.

Sample Input 2

3 3 3
###
#S#
###

Sample Output 2

2

Takahashi cannot move in the first cast, but can unlock room (1,2).
Then, he can move to room (1,2) in the next cast, achieving the objective in two casts.

Sample Input 3

7 7 2
#######
#######
##...##
###S###
##.#.##
###.###
#######

Sample Output 3

2

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

// package atcoder.agc.agc014;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {

    private static final int INF = 10000000;
    private static int[] dx = new int[]{0, -1, 0, 1};
    private static int[] dy = new int[]{-1, 0, 1, 0};


    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int h = in.nextInt();
        int w = in.nextInt();
        int k = in.nextInt();

        char[][] maze = new char[h][];
        int sy = 0;
        int sx = 0;
        for (int i = 0; i < h ; i++) {
            maze[i] = in.nextToken().toCharArray();
            for (int j = 0; j < w ; j++) {
                if (maze[i][j] == 'S') {
                    sy = i;
                    sx = j;
                }
            }
        }

        int[] que = new int[2000000];
        int qh = 0;
        int qt = 0;
        int[][] dp = new int[h][w];
        for (int i = 0; i < h ; i++) {
            Arrays.fill(dp[i], INF);
        }
        dp[sy][sx] = 0;
        que[qh++] = sy;
        que[qh++] = sx;
        while (qt < qh) {
            int ny = que[qt++];
            int nx = que[qt++];
            int tt = dp[ny][nx]+1;
            for (int d = 0 ;  d < 4 ; d++) {
                int ty = ny+dy[d];
                int tx = nx+dx[d];
                if (ty < 0 || tx < 0 || ty >= h || tx >= w || maze[ty][tx] == '#') {
                    continue;
                }
                if (dp[ty][tx] > tt) {
                    dp[ty][tx] = tt;
                    que[qh++] = ty;
                    que[qh++] = tx;
                }
            }
        }

        int best = INF;
        for (int i = 0; i < h ; i++) {
            for (int j = 0; j < w ; j++) {
                int distToOut = Math.min(Math.min(i+1, h-i), Math.min(j+1, w-j));
                if (maze[i][j] == '#') {
                    for (int d = 0 ; d < 4 ; d++) {
                        int ty = i+dy[d];
                        int tx = j+dx[d];
                        if (ty < 0 || tx < 0 || ty >= h || tx >= w || maze[ty][tx] == '#') {
                            continue;
                        }
                        int come = dp[ty][tx];
                        if (come <= k) {
                            best = Math.min(best, 1 + (distToOut + k - 1) / k);
                        } else {
                            int totalCost = come + distToOut;
                            best = Math.min(best, (totalCost + k - 1) / k);
                        }
                    }
                } else {
                    int come = dp[i][j];
                    if (i == 0 || i == h-1 || j == 0 || j == w-1) {
                        best = Math.min(best, (come + k - 1) / k);
                    }
                }
            }
        }

        out.println(best);
        out.flush();
    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int[] nextInts(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }

        private int[][] nextIntTable(int n, int m) {
            int[][] ret = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i][j] = nextInt();
                }
            }
            return ret;
        }

        private long[] nextLongs(int n) {
            long[] ret = new long[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextLong();
            }
            return ret;
        }

        private long[][] nextLongTable(int n, int m) {
            long[][] ret = new long[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i][j] = nextLong();
                }
            }
            return ret;
        }

        private double[] nextDoubles(int n) {
            double[] ret = new double[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextDouble();
            }
            return ret;
        }

        private int next() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            if ('a' <= c && c <= 'z') {
                return (char) c;
            }
            if ('A' <= c && c <= 'Z') {
                return (char) c;
            }
            throw new InputMismatchException();
        }

        public String nextToken() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res*sgn;
        }

        public long nextLong() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res*sgn;
        }

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}