Problem:
Score: 400 points

Problem statement

We have an H \times W grid whose squares are painted black or white. The square at the i-th row from the top and the j-th column from the left is denoted as (i, j).

Snuke would like to play the following game on this grid. At the beginning of the game, there is a character called Kenus at square (1, 1). The player repeatedly moves Kenus up, down, left or right by one square. The game is completed when Kenus reaches square (H, W) passing only white squares.

Before Snuke starts the game, he can change the color of some of the white squares to black. However, he cannot change the color of square (1, 1) and (H, W). Also, changes of color must all be carried out before the beginning of the game.

When the game is completed, Snuke's score will be the number of times he changed the color of a square before the beginning of the game. Find the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed, that is, Kenus can never reach square (H, W) regardless of how Snuke changes the color of the squares.

The color of the squares are given to you as characters s_{i, j}. If square (i, j) is initially painted by white, s_{i, j} is .; if square (i, j) is initially painted by black, s_{i, j} is #.

Constraints

H is an integer between 2 and 50 (inclusive).

W is an integer between 2 and 50 (inclusive).

s_{i, j} is . or # (1 \leq i \leq H, 1 \leq j \leq W).

s_{1, 1} and s_{H, W} are ..

Input

Input is given from Standard Input in the following format:

H W
s_{1, 1}s_{1, 2}s_{1, 3} ... s_{1, W}
s_{2, 1}s_{2, 2}s_{2, 3} ... s_{2, W}
: :
s_{H, 1}s_{H, 2}s_{H, 3} ... s_{H, W}

Output

Print the maximum possible score that Snuke can achieve, or print -1 if the game cannot be completed.

Sample Input 1

3 3
..#
#..
...

Sample Output 1

2

The score 2 can be achieved by changing the color of squares as follows:

Sample Input 2

10 37
.....................................
...#...####...####..###...###...###..
..#.#..#...#.##....#...#.#...#.#...#.
..#.#..#...#.#.....#...#.#...#.#...#.
.#...#.#..##.#.....#...#.#.###.#.###.
.#####.####..#.....#...#..##....##...
.#...#.#...#.#.....#...#.#...#.#...#.
.#...#.#...#.##....#...#.#...#.#...#.
.#...#.####...####..###...###...###..
.....................................

Sample Output 2

209

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

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int h = cin.Int();
			int w = cin.Int();
			var s = new string[h];
			for (int i = 0; i < h; i++) {
				s[i] = cin.Next();
			}

			var d = new DXY[h, w];
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					d[i, j] = new DXY { D = int.MaxValue, PX = -1, PY = -1 };
				}
			}

			d[0, 0] = new DXY { D = 0, PX = -1, PY = -1 };
			var q = new Queue<Tuple<int, int>>();
			q.Enqueue(new Tuple<int, int>(0, 0));
			int[] delta = { 1, 0, -1, 0, 1 };
			while (q.Count > 0) {
				var cur = q.Dequeue();
				int i = cur.Item1;
				int j = cur.Item2;
				for (int n = 0; n < 4; n++) {
					int ii = i + delta[n];
					int jj = j + delta[n + 1];
					if (ii >= 0 && jj >= 0 && ii < h && jj < w) {
						if (s[ii][jj] == '#') {
							continue;
						}

						if (d[ii, jj].D > d[i, j].D + 1) {
							d[ii, jj] = new DXY { D = d[i, j].D + 1, PY = i, PX = j };
							q.Enqueue(new Tuple<int, int>(ii, jj));
						}
					}
				}
			}

			if (d[h - 1, w - 1].D == int.MaxValue) {
				Console.WriteLine(-1);
				return;
			}

			var root = new bool[h, w];
			root[0, 0] = true;
			root[h - 1, w - 1] = true;
			int nx = d[h - 1, w - 1].PX;
			int ny = d[h - 1, w - 1].PY;
			while (nx >= 0 && ny >= 0) {
				root[ny, nx] = true;
				int nnx = d[ny, nx].PX;
				int nny = d[ny, nx].PY;
				nx = nnx;
				ny = nny;
			}

			int ans = 0;
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					if (s[i][j] == '.' && root[i, j] == false) {
						++ans;
					}
				}
			}

			Console.WriteLine(ans);
		}

		struct DXY
		{
			public int D { get; set; }
			public int PX { get; set; }
			public int PY { get; set; }
		}
	}

	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private readonly Func<string> reader_;
		private string[] buf_;
		private int index_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}