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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using CompLib.Util;

public class Program
{
    int H, W, K;
    string[] A;
    int[] dx = new int[] { 0, 0, 1, -1 };
    int[] dy = new int[] { 1, -1, 0, 0 };
    public void Solve()
    {
        var sc = new Scanner();
        H = sc.NextInt();
        W = sc.NextInt();
        K = sc.NextInt();
        A = new string[H];
        for (int i = 0; i < H; i++)
        {
            A[i] = sc.Next();
        }


        // SからK回以内の移動　端までの距離 最小


        var d = new int[H, W];
        for (int i = 0; i < H; i++)
        {
            for (int j = 0; j < W; j++)
            {
                d[i, j] = int.MaxValue;
            }
        }

        int sy = -1;
        int sx = -1;
        for (int i = 0; i < H; i++)
        {
            for (int j = 0; j < W; j++)
            {
                if (A[i][j] == 'S')
                {
                    sy = i;
                    sx = j;
                    break;
                }
            }
            if (sy != -1) break;
        }

        var yq = new Queue<int>();
        var xq = new Queue<int>();

        yq.Enqueue(sy);
        xq.Enqueue(sx);
        d[sy, sx] = 0;
        while (yq.Count > 0)
        {
            var yy = yq.Dequeue();
            var xx = xq.Dequeue();
            for (int i = 0; i < 4; i++)
            {
                int ny = yy + dy[i];
                int nx = xx + dx[i];
                if (ny < 0 || ny >= H) continue;
                if (nx < 0 || nx >= W) continue;
                if (d[ny, nx] <= d[yy, xx] + 1) continue;
                if (d[yy, xx] + 1 > K) continue;
                if (A[ny][nx] == '#') continue;
                d[ny, nx] = d[yy, xx] + 1;
                yq.Enqueue(ny);
                xq.Enqueue(nx);
            }
        }

        int ans = int.MaxValue;

        for (int i = 0; i < H; i++)
        {
            for (int j = 0; j < W; j++)
            {
                if (d[i, j] != int.MaxValue)
                {
                    int yy = Math.Min(i, H - 1 - i);
                    int xx = Math.Min(j, W - 1 - j);
                    ans = Math.Min(ans, 1 + (Math.Min(yy, xx) + K - 1) / K);
                }
            }
        }
        Console.WriteLine(ans);
    }


    public static void Main(string[] args) => new Program().Solve();
}

namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}