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

namespace atcoder
{
	class Program
	{
		static int In => int.Parse(Console.ReadLine());
		static int[] Ins => Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
		static void Out(bool b) => Console.WriteLine(b ? "Yes" : "No");

		static string[] map;
		static int H, W;

		static void Main(string[] args)
		{
			var input = Ins;
			H = input[0];
			W = input[1];
			map = new string[input[0]];
			for(int i = 0;i < input[0];i++)
			{
				map[i] = Console.ReadLine();
			}
			
			Node n = new Node(new IntPoint(1, 1), 0,new IntPoint[0]);
			Node ans = (Node)DijkstrasAlgorithm(n);
			if (ans == null) Console.WriteLine(-1);
			else
			{
				List<IntPoint> li = new List<IntPoint>(ans.route);
				int sum = 0;
				for (int i = 0; i < H; i++)
				{
					for (int j = 0; j < W; j++)
					{
						if (map[i][j] == '.')
						{
							int id = li.IndexOf(new IntPoint(j + 1, i + 1));
							if (id == -1) sum++;
						}
					}
				}
				Console.WriteLine(sum);
			}
		}

		/// <summary>
		/// ダイクストラのアルゴリズム
		/// </summary>
		/// <param name="start"></param>
		/// <param name="max">最大化問題を解く</param>
		/// <returns></returns>
		public static INodeEv DijkstrasAlgorithm(INodeEv start, bool max = false)
		{
			var pque = new PriorityQueue<INodeEv>(max);
			var visited = new HashSet<Node>();
			pque.Push(start);
			visited.Add((Node)start);
			while (pque.Length != 0)
			{
				var item = pque.Pop();
				if (item.IsGoal()) return item;
				foreach (var next in item.GetNext())
				{
					if (!visited.Contains(next))
					{
						visited.Add((Node)next);
						pque.Push(next);
					}
				}
			}
			return null;
		}

		public class Node : INodeEv
		{
			IntPoint p;
			int dis;
			public IntPoint[] route;

			public override bool Equals(object obj)
			{
				return this.p.X == ((Node)obj).p.X && this.p.Y == ((Node)obj).p.Y;
			}

			public Node(IntPoint pp,int d,IntPoint[] r)
			{
				p = pp;
				dis = d;
				List<IntPoint> li = new List<IntPoint>(r);
				li.Add(pp);
				route = li.ToArray();
			}

			public int CompareTo(object obj)
			{
				var i = dis.CompareTo(((Node)obj).dis);
				if (i == 0) return p.CompareTo(((Node)obj).p);
				else return i;
			}

			public override int GetHashCode()
			{
				return this.p.GetHashCode();
			}

			public bool Equals(INodeEv x, INodeEv y)
			{
				return ((Node)x).p.Equals(((Node)y).p);
			}

			public int GetHashCode(INodeEv obj)
			{
				return p.GetHashCode();
			}

			public IEnumerable<INodeEv> GetNext()
			{
				var pp = p + new IntPoint(0, 1);
				if (isin(pp)) yield return new Node(pp, dis + 1,route);
				pp = p + new IntPoint(0, -1);
				if (isin(pp)) yield return new Node(pp, dis + 1,route);
				pp = p + new IntPoint(1, 0);
				if (isin(pp)) yield return new Node(pp, dis + 1,route);
				pp = p + new IntPoint(-1, 0);
				if (isin(pp)) yield return new Node(pp, dis + 1,route);
			}

			bool isin(IntPoint pos)
			{
				return 1 <= pos.X && pos.X <= W && 1 <= pos.Y && pos.Y <= H && map[pos.Y-1][pos.X-1] != '#';
			}

			public bool IsGoal()
			{
				return p.X == W && p.Y == H;
			}
		}

		public interface INodeEv : IComparable, IEqualityComparer<INodeEv>
		{
			bool IsGoal();
			IEnumerable<INodeEv> GetNext();
		}
	}

	/// <summary>
	/// 優先度付きキューを提供する
	/// </summary>
	/// <typeparam name="T"></typeparam>
	public class PriorityQueue<T> where T : IComparable
	{
		#region member
		private List<T> list;
		private bool reverse;
		#endregion

		#region constructor
		/// <summary>
		/// 
		/// </summary>
		/// <param name="isReverse">定義された順序の逆で評価する</param>
		public PriorityQueue(bool isReverse = false)
		{
			list = new List<T>();
			reverse = isReverse;
		}
		#endregion

		#region private method
		private bool compare(T a, T b)
		{
			return reverse ^ a.CompareTo(b) > 0;
		}

		private void swap(int a, int b)
		{
			T tmp = list[a];
			list[a] = list[b];
			list[b] = tmp;
		}
		#endregion

		#region public method
		/// <summary>
		/// 要素を追加する
		/// </summary>
		/// <param name="item">追加する要素</param>
		public void Push(T item)
		{
			if (Length < list.Count) list[Length] = item;
			else list.Add(item);
			var pos = Length++;
			while (pos != 0)
			{
				var parent = (pos + 1) / 2 - 1;
				if (compare(list[pos], list[parent])) break;
				swap(pos, parent);
				pos = parent;
			}
		}

		/// <summary>
		/// 要素を追加する
		/// </summary>
		/// <param name="items">追加する要素の列</param>
		public void Push(IEnumerable<T> items)
		{
			foreach (var item in items)
			{
				Push(item);
			}
		}

		/// <summary>
		/// 値を確認する
		/// </summary>
		/// <returns></returns>
		public T Peek()
		{
			return list[0];
		}

		/// <summary>
		/// 値を取り出す
		/// </summary>
		/// <returns></returns>
		public T Pop()
		{
			var ret = Peek();
			var pos = 0;
			list[0] = list[--Length];
			while (2 * pos + 1 < Length)
			{
				var child = 2 * pos + 1;
				var child_other = 2 * pos + 2;
				if (child_other < Length && compare(list[child], list[child_other]))
				{
					child = child_other;
				}
				if (compare(list[child], list[pos])) break;
				swap(pos, child);
				pos = child;
			}
			return ret;
		}

		/// <summary>
		/// クリアする
		/// </summary>
		public void Clear()
		{
			list.Clear();
		}
		#endregion

		#region property
		/// <summary>
		/// 要素の長さを取得する
		/// </summary>
		public int Length
		{
			get;
			private set;
		}
		#endregion
	}

	public class IntPoint : IComparable, ICloneable
	{
		#region member
		public int X
		{
			get;
			private set;
		}
		public int Y
		{
			get;
			private set;
		}
		#endregion

		#region constructor
		public IntPoint(int x, int y)
		{
			X = x;
			Y = y;
		}

		public IntPoint()
		{
			X = 0;
			Y = 0;
		}
		#endregion

		#region operator
		public static IntPoint operator +(IntPoint a, IntPoint b)
		{
			return new IntPoint(a.X + b.X, a.Y + b.Y);
		}

		public static IntPoint operator -(IntPoint a, IntPoint b)
		{
			return new IntPoint(a.X - b.X, a.Y - b.Y);
		}
		public static bool operator ==(IntPoint a, IntPoint b)
		{
			return a.X == b.X && a.Y == b.Y;
		}
		public static bool operator !=(IntPoint a, IntPoint b)
		{
			return !(a == b);
		}
		public static bool operator >(IntPoint a, IntPoint b)
		{
			if (a.X != b.X) return a.X > b.Y;
			else return a.Y > b.Y;
		}
		public static bool operator >=(IntPoint a, IntPoint b)
		{
			return a == b || (a > b);
		}
		public static bool operator <(IntPoint a, IntPoint b)
		{
			return !(a >= b);
		}
		public static bool operator <=(IntPoint a, IntPoint b)
		{
			return !(a > b);
		}
		#endregion

		#region public method
		/// <summary>
		/// マンハッタン距離を取得する
		/// </summary>
		/// <param name="a"></param>
		/// <param name="b"></param>
		/// <returns></returns>
		public static int GetManhattanDistance(IntPoint a, IntPoint b)
		{
			return Math.Abs(a.X - b.X) + Math.Abs(a.Y - b.Y);
		}

		/// <summary>
		/// ユークリッド距離を取得する
		/// </summary>
		/// <param name="a"></param>
		/// <param name="b"></param>
		/// <returns></returns>
		public static double GetEuclideanDistance(IntPoint a, IntPoint b)
		{
			var tmp = a - b;
			return Math.Sqrt(tmp.X * tmp.X + tmp.Y * tmp.Y);
		}
		#endregion

		#region override or implementation
		public int CompareTo(object obj)
		{
			if (X != ((IntPoint)obj).X) return X.CompareTo(((IntPoint)obj).X);
			else return Y.CompareTo(((IntPoint)obj).Y);
		}

		public override bool Equals(object obj)
		{
			return this.X == ((IntPoint)obj).X && this.Y == ((IntPoint)obj).Y;
		}

		public override int GetHashCode()
		{
			return X.GetHashCode() + (Y.GetHashCode() << 1);
		}

		public object Clone()
		{
			return new IntPoint(X, Y);
		}
		#endregion
	}
}