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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"container/heap"
	"fmt"
	"math"
	"os"
)

var white = "."
var isNotPath = -1

func main() {
	rdr := NewReader(10)
	height, width := ReadInt(), ReadInt()

	whiteCount := 0
	lines := make([]string, height)
	for i := range lines {
		lines[i] = ReadLine(rdr)
	}

	s := make([][]int, height)
	for i, line := range lines {
		l := make([]int, width)
		for j := 0; j < len(line); j++ {
			if line[j:j+1] == white {
				l[j] = whiteCount
				whiteCount++
			} else {
				l[j] = isNotPath
			}
		}
		s[i] = l
	}

	inRange := func(i, j int) bool {
		return 0 <= i && i < height && 0 <= j && j < width
	}

	var edges []EdgeD
	for i, line := range s {
		for j, cell := range line {
			if cell == isNotPath {
				continue
			}
			if inRange(i+1, j) && s[i+1][j] != isNotPath {
				edges = append(edges, EdgeD{From: cell, To: s[i+1][j], Distance: 1})
			}
			if inRange(i-1, j) && s[i-1][j] != isNotPath {
				edges = append(edges, EdgeD{From: cell, To: s[i-1][j], Distance: 1})
			}
			if inRange(i, j+1) && s[i][j+1] != isNotPath {
				edges = append(edges, EdgeD{From: cell, To: s[i][j+1], Distance: 1})
			}
			if inRange(i, j-1) && s[i][j-1] != isNotPath {
				edges = append(edges, EdgeD{From: cell, To: s[i][j-1], Distance: 1})
			}
		}
	}

	goal := s[height-1][width-1]
	connected, distance := Dijkstra(edges, 0, goal)

	if !connected {
		fmt.Println(isNotPath)
		return
	}
	fmt.Println(goal - distance)
	return
}

type Reader struct {
	rdr  *bufio.Reader
	size int
}

func NewReader(size int) *Reader {
	return &Reader{
		bufio.NewReaderSize(os.Stdin, size),
		size,
	}
}

func ReadInt() (i int) {
	fmt.Scan(&i)
	return
}

func ReadLine(r *Reader) string {
	buf := make([]byte, 0, r.size)
	for {
		line, isPrefix, err := r.rdr.ReadLine()
		if err != nil {
			panic(err)
		}
		buf = append(buf, line...)
		if !isPrefix {
			break
		}
	}
	return string(buf)
}

type EdgeD struct {
	From     int
	To       int
	Distance int
}

type Cost struct {
	to       int
	priority int
	index    int
}

func Dijkstra(edges []EdgeD, start, goal int) (connected bool, cost int) {
	if len(edges) == 0 {
		return
	}

	// initialize
	max := math.MaxInt32
	distances := make(map[int]int)
	for _, e := range edges {
		distances[e.From] = max
		distances[e.To] = max
	}

	pq := make(EdgePriorityQueue, 0)
	heap.Init(&pq)

	// solve
	distances[start] = 0
	heap.Push(&pq, &Cost{to: start, priority: 0})

	for pq.Len() > 0 {
		cost := heap.Pop(&pq).(*Cost)
		if distances[cost.to] < cost.priority {
			continue
		}
		for _, e := range edges {
			c := distances[e.From] + e.Distance
			if distances[e.From] != max && distances[e.To] > c {
				distances[e.To] = c
				heap.Push(&pq, &Cost{to: e.To, priority: c})
			}
		}
	}

	if distances[goal] != max {
		connected = true
	}
	cost = distances[goal]

	return
}

type EdgePriorityQueue []*Cost

func (pq EdgePriorityQueue) Len() int { return len(pq) }
func (pq EdgePriorityQueue) Less(i, j int) bool {
	return pq[i].priority < pq[j].priority
}
func (pq EdgePriorityQueue) Swap(i, j int) {
	pq[i], pq[j] = pq[j], pq[i]
	pq[i].index = i
	pq[j].index = j
}
func (pq *EdgePriorityQueue) Push(x interface{}) {
	n := len(*pq)
	item := x.(*Cost)
	item.index = n
	*pq = append(*pq, item)
}
func (pq *EdgePriorityQueue) Pop() interface{} {
	old := *pq
	n := len(old)
	item := old[n-1]
	item.index = -1 // for safety
	*pq = old[0 : n-1]
	return item
}
func (pq *EdgePriorityQueue) update(item *Cost, to, distance int) {
	item.to = to
	item.priority = distance
	heap.Fix(pq, item.index)
}