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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder2 {
	class Program {
		static void Main(string[] args) {

			var inputArray = retreiveLongArray();
			var inputCount = 2;

			// 不正な入力は処理しない
			if (inputArray.Length != inputCount) {
				Console.WriteLine("invalid input");
				return;
			}
			int H = (int)inputArray[0]-1;
			int W =(int) inputArray[1]-1;

			//マスを作る
			var masu = new List<int[]>();

			for (int i = 0; i <= H; i++) {

				var inpStr = retreiveStringArray()[0];
				var intArray = inpStr.Select(x => {
					return x == '.' ? 0 : 1;
				}).ToArray();
				masu.Add(intArray);

			}
			//白ますの数を数える
			var shiroCount = 0;
			foreach (var arr in masu) {
				shiroCount += arr.Where(x => x == 0).Count();
			}

			//最短経路のマス数を格納
			_saitankeiro = int.MaxValue;
			_bestWay = new Dictionary<string, int>();
			var keiroStack = new Stack<string>();

			//DFSで全経路を探索
			DFS(H, W, 0, 0, keiroStack, masu,"-1_-1");


			//答えの出力
			var ans = _saitankeiro == int.MaxValue ? -1: shiroCount - _saitankeiro;
			Console.WriteLine(ans);

		}
		/// <summary>
		/// 最短経路を格納
		/// </summary>
		private static int _saitankeiro;

		/// <summary>
		/// 最短経路を格納
		/// </summary>
		private static Dictionary<string,int> _bestWay;

		private static void DFS(int H,int W,int h,int w,Stack<string> keirostack,List<int[]> masu,string previous) {

			var positionStr = h + "_" + w;

			//範囲外の場合も探索しない
			if (h < 0 | H < h) {
				return;
			}
			//範囲外の場合も探索しない
			if (w < 0 | W < w) {
				return;
			}
			//障害物があった場合も探索しない
			if (masu[h][w] == 1) {
				return;
			}

			//初めての到達か、最短で到達した場合のみ調査続行
			if (_bestWay.ContainsKey(positionStr)) {
				var best = _bestWay[positionStr];
				if(best <= keirostack.Count()) {
					return;
				}
				_bestWay[positionStr] = keirostack.Count();
			}
			else {
				_bestWay.Add(positionStr, keirostack.Count());
			}


			//到達した場合
			if (h==H && w == W) {
				_saitankeiro = Math.Min(_saitankeiro, keirostack.Count()+1);
				return;
			}


			keirostack.Push(positionStr);

			var nextPositons = new List<Tuple<int, int>> {
				Tuple.Create(h+1,w),
				Tuple.Create(h,w+1),
				Tuple.Create(h-1,w),
				Tuple.Create(h,w-1),
			};
			foreach (var posi in nextPositons) {
				var nextposition = posi.Item1 + "_" + posi.Item2;
				if (nextposition == previous) {
					continue;
				}

				DFS(H, W, posi.Item1, posi.Item2, keirostack,masu,positionStr);
			}

			keirostack.Pop();
		}


		/// <summary>
		/// スペースで区切られた文字列配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static string[] retreiveStringArray() {
			var inputArray = Console.ReadLine().Split(' ');
			return inputArray;
		}

		/// <summary>
		/// スペースで区切られた整数配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static long[] retreiveLongArray() {
			var inputArray = Console.ReadLine().Split(' ');
			var longArray = inputArray.Select(s => long.Parse(s));
			return longArray.ToArray();
		}
	}
}