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 Java (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;
public class Main {
 
  public static void main(String[] args) { 
      //int t = sc.nextInt();
      //while(t-- > 0) 
        solve();
      out.close();
  }
  static int MAX_SIZE = 100;
  private static void solve() {
      
      int n = sc.nextInt();
      int m = sc.nextInt();
      char[][] grid = new char[n][m];
      for(int i = 0; i < n; i++)
          grid[i] = sc.next().toCharArray();
      if(grid[0][0] == '#' || grid[n-1][m-1] == '#') {
        out.println(-1);
        return;
      }
      int minSteps = 0;
      boolean canReach = false;

      int[] rows = new int[]{-1, 1, 0, 0};
      int[] cols = new int[]{0, 0, -1, 1};
      Queue<Integer> queue = new LinkedList<>();
      queue.offer(0);
      Set<Integer> visited = new HashSet<>();
      visited.add(0);
      outer:
      while(queue.size() > 0) {
        int size = queue.size();
        for(int i = 0; i < size; i++) {
          int pos = queue.poll();
          int row = pos / MAX_SIZE;
          int col = pos % MAX_SIZE;
          if(row == n-1 && col == m-1) {
            canReach = true;
            break outer;
          }
          for(int r = 0; r < rows.length; r++) {
            int nr = row + rows[r];
            int nc = col + cols[r];
            if(isValid(grid, visited, nr, nc)) {
              queue.offer(nr * MAX_SIZE + nc);
              visited.add(nr * MAX_SIZE + nc);
            }
          }
        }
        minSteps++;
      }
      if(!canReach)
        out.println(-1);
      int cnt = 0;
      for(int i = 0; i < n; i++) {
        for(int j = 0; j < m; j++){
          if(grid[i][j] == '#')
            cnt++;
        }
      }
      out.println(n * m - 1 - cnt - minSteps);
  }


  private static boolean isValid(char[][] grid, Set<Integer> visited, int row, int col) {
    if(row < 0 || row >= grid.length || col < 0 || col >= grid[row].length || grid[row][col] == '#' || visited.contains(row * MAX_SIZE + col))
      return false;
    return true;
  }
  public static void sort(int[] a) {
    int l = 0, r = a.length;
      ArrayList<Integer> list=new ArrayList<>();
      for (int i=l ; i<r; i++) list.add(a[i]);
      Collections.sort(list);
      for (int i=l; i<r; i++) a[i]=list.get(i-l);
  }

  private static String mkArr(int[] arr) {
    StringBuilder sb = new StringBuilder();
    for(int a : arr) {
      sb.append(a + " ");
    }
    return sb.toString();
  }

  private static String mkList(List<Integer> arr) {
    StringBuilder sb = new StringBuilder();
    for(int a : arr) {
      sb.append(a + " ");
    }
    return sb.toString();
  }

  private static int gcd(int a, int b) {
    if(b == 0) return a;
    return gcd(b, a % b);
  }
  
  static int mod = 1_000_000_007;

  private static long C(int n, int k) {
    long res1 = factor(n-k+1, n);
    long res2 = factor(1, k);
    long reverse = reverse(res2);
    return (res1 * reverse) % mod;
  }

  private static long reverse(long a) {
    return powMod(a, mod - 2);
  }

  private static long factor(int left, int right){
    long res = 1;
    for(int i = left; i <= right; i++)
      res = (res * i) % mod;
    return res;
  }

  public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
 
  public static FastScanner sc = new FastScanner();

  static class FastScanner {
      BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
      StringTokenizer st=new StringTokenizer("");
      String next() {
        while (!st.hasMoreTokens())
          try {
            st=new StringTokenizer(br.readLine());
          } catch (IOException e) {
            e.printStackTrace();
          }
        return st.nextToken();
      }
      
      int nextInt() {
        return Integer.parseInt(next());
      }
      int[] readArray(int n) {
        int[] a=new int[n];
        for (int i=0; i<n; i++) a[i]=nextInt();
        return a;
      }
      long nextLong() {
        return Long.parseLong(next());
      }
  }

  static long pow(long a, long N) {
    if (N == 0) return 1;
    else if (N == 1) return a;
    else {
      long R = pow(a,N/2);
      if (N % 2 == 0) {
        return R*R;
      }
      else {
        return R*R*a;
      }
    }
  }
   
  static long powMod(long a, long N) {
    if (N == 0) return 1;
    else if (N == 1) return a % mod;
    else {
      long R = powMod(a,N/2) % mod;
      R = (R * R) % mod;
      if (N % 2 == 1) {
        R = (R * a) % mod;
      }
        return R % mod;
    }
  }

  static void mergeSort(int[] A){ // low to hi sort, single array only
    int n = A.length;
    if (n < 2) return;
    int[] l = new int[n/2];
    int[] r = new int[n - n/2];

    for (int i = 0; i < n/2; i++){
      l[i] = A[i];
    }

    for (int j = n/2; j < n; j++){
      r[j-n/2] = A[j];
    }

    mergeSort(l);
    mergeSort(r);
    merge(l, r, A);
  }
 
  static void merge(int[] l, int[] r, int[] a){
    int i = 0, j = 0, k = 0;
    while (i < l.length && j < r.length && k < a.length){
      if (l[i] < r[j]){
        a[k] = l[i];
        i++;
      }
      else{
        a[k] = r[j];
        j++;
      }
      k++;
    }
    while (i < l.length){
      a[k] = l[i];
      i++;
      k++;
    }

    while (j < r.length){
      a[k] = r[j];
      j++;
      k++;
    }
  }

  private static class Edge {
    int src;
    int dest;
    int weight;
    public Edge(int s, int d, int w) {
      this.src = s;
      this.dest = d;
      this.weight = w;
    }
  }

  private static int[] prim(Map<Integer, List<Edge>> graph) {
      int n = graph.size(); // number of the nodes
      Edge[] edges = new Edge[n];
      for(int i = 0; i < n; i++)
        edges[i] = new Edge(-1, i, Integer.MAX_VALUE);
      edges[0].weight = 0;

      int[] parents = new int[n];
      parents[0] = -1;

      TreeSet<Edge> treeSet = new TreeSet<>((a, b) -> a.weight - b.weight);
      treeSet.add(edges[0]);

      boolean[] visited = new boolean[n];
      while(treeSet.size() > 0) {
        Edge e = treeSet.pollFirst();
        visited[e.dest] = true;
        for(Edge child : graph.get(e.dest)) {
          if(visited[child.dest]) continue;
          if(edges[child.dest].weight > child.weight) {
            treeSet.remove(edges[child.dest]);
            edges[child.dest].weight = child.weight;
            treeSet.add(edges[child.dest]);
            parents[child.dest] = e.dest;
          }
        }
      }
      return parents;
  }

  private static void testDijkstr() {
    Map<Integer, List<Edge>> graph = new HashMap<>();
    for(int i = 0; i < 9; i++)
      graph.put(i, new ArrayList<>());
    addEdge(0, 1, 4 , graph);
    addEdge(0, 7, 8 , graph);
    addEdge(1, 2, 8 , graph);
    addEdge(1, 7, 11, graph);
    addEdge(2, 3, 7 , graph);
    addEdge(2, 8, 2 , graph);
    addEdge(2, 5, 4 , graph);
    addEdge(3, 4, 9 , graph);
    addEdge(3, 5, 14, graph);
    addEdge(4, 5, 10, graph);
    addEdge(5, 6, 2 , graph);
    addEdge(6, 7, 1 , graph);
    addEdge(6, 8, 6 , graph);
    addEdge(7, 8, 7 , graph);
    Edge[] es = dijkstra(graph);
    for(int i = 0; i < 9; i++)
    out.println(i + ": " + es[i].weight);
  }

  private static void addEdge(int a, int b, int w, Map<Integer, List<Edge>> graph) {
    graph.get(a).add(new Edge(a, b, w));
    graph.get(b).add(new Edge(b, a, w));
  }

  private static Edge[] dijkstra(Map<Integer, List<Edge>> graph) {
    int n = graph.size();
    Edge[] es =  new Edge[n];
    for(int i = 0; i < n; i++)
      es[i] = new Edge(-1, i, Integer.MAX_VALUE);
    es[0].weight = 0;

    TreeSet<Edge> treeSet = new TreeSet<>((a, b) -> a.weight - b.weight);
    treeSet.add(es[0]);

    boolean[] visited = new boolean[n];

    while(treeSet.size() > 0) {
      Edge e = treeSet.pollFirst();
      visited[e.dest] = true;
      for(Edge ed : graph.get(e.dest)) {
        if(visited[ed.dest] || ed.weight + es[e.dest].weight >= es[ed.dest].weight) 
          continue;
        treeSet.remove(es[ed.dest]);
        es[ed.dest].weight = ed.weight + es[e.dest].weight;
        treeSet.add(es[ed.dest]);
      }
    }
    return es;
  }

  private static Edge[] kruskal(int v, Edge[] edges) {
    Edge[] res = new Edge[v-1];

    int[] p = new int[v];
    for(int i = 0; i < v; i++) 
      p[i] = i;

    int[] rank = new int[v];
    Arrays.fill(rank, 1);

    Arrays.sort(edges, (e1, e2) -> e1.weight - e2.weight);
    for(int i = 0, idx = 0; i < res.length;) {
      Edge e = edges[idx++];
      if(union(p, rank, e.src, e.dest)) {
        res[i++] = e;
      }
    }
    return res;
  }

  private static boolean union(int[] root, int[] rank, int u, int v) {
      int rootA = find(root, u);
      int rootB = find(root, v);
      if(rootA == rootB) return false;

      if(rank[rootA] > rank[rootB]) {
        rank[rootA] += rank[rootB];
        root[rootB] = rootA;
      } else {
        rank[rootB] += rank[rootA];
        root[rootA] = rootB;
      }
      return true;
  }

  private static int find(int[] root, int node) {
    if(root[node] != node) {
      root[node] = find(root, root[node]);
    }
    return root[node];
  }

  static class BIT {
    int n;
    int[] nums;
    int[] bit;

    public BIT(int[] nums) {
      this.nums = nums;
      this.n = nums.length;
      this.bit = new int[n + 1];
      for(int i = 0; i < n; i++)
        init(i, nums[i]);
    }

    void init(int i, int val) {
      i++;
      while(i <= n) {
        bit[i] += val;
        i += (i & -i); // (i & (-i)): get moet least significate digit
      }
    }

    void update(int i, int val) {
      int diff = val - nums[i];
      nums[i] = val;
      init(i, diff);
    }

    int getSum(int i) {
      int sum = 0;
      i++;
      while(i > 0) {
        sum += bit[i];
        i -= (i & -i); // ex: 1100 -> 1000 -> 0000. subtract moet least significate digit
      }
      return sum;
    }

    int sumRange(int i, int j) {
      return getSum(j) - getSum(i - 1);
    }
  }
}