Problem:
Score : 200 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

We have a grid of H rows and W columns. Initially, there is a stone in the top left cell. Shik is trying to move the stone to the bottom right cell. In each step, he can move the stone one cell to its left, up, right, or down (if such cell exists). It is possible that the stone visits a cell multiple times (including the bottom right and the top left cell).

You are given a matrix of characters a_{ij} (1 \leq i \leq H, 1 \leq j \leq W). After Shik completes all moving actions, a_{ij} is # if the stone had ever located at the i-th row and the j-th column during the process of moving. Otherwise, a_{ij} is .. Please determine whether it is possible that Shik only uses right and down moves in all steps.

Constraints

2 \leq H, W \leq 8

a_{i,j} is either # or ..

There exists a valid sequence of moves for Shik to generate the map a.

Input

The input is given from Standard Input in the following format:

H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}

Output

If it is possible that Shik only uses right and down moves, print Possible. Otherwise, print Impossible.

Sample Input 1

4 5
##...
.##..
..##.
...##

Sample Output 1

Possible

The matrix can be generated by a 7-move sequence: right, down, right, down, right, down, and right.

Sample Input 2

5 3
###
..#
###
#..
###

Sample Output 2

Impossible

Sample Input 3

4 5
##...
.###.
.###.
...##

Sample Output 3

Impossible

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
	"strings"
)

type bufReader struct {
	r   *bufio.Reader
	buf []byte
	i   int
}

var reader = &bufReader{
	bufio.NewReader(os.Stdin),
	make([]byte, 0),
	0,
}

func (r *bufReader) readLine() {
	if r.i < len(r.buf) {
		return
	}
	r.buf = make([]byte, 0)
	r.i = 0
	for {
		line, isPrefix, err := r.r.ReadLine()
		if err != nil {
			panic(err)
		}
		r.buf = append(r.buf, line...)
		if !isPrefix {
			break
		}
	}
}

func (r *bufReader) next() string {
	r.readLine()
	from := r.i
	for ; r.i < len(r.buf); r.i++ {
		if r.buf[r.i] == ' ' {
			break
		}
	}
	s := string(r.buf[from:r.i])
	r.i++
	return s
}

func (r *bufReader) nextLine() string {
	r.readLine()
	s := string(r.buf[r.i:])
	r.i = len(r.buf)
	return s
}

var writer = bufio.NewWriter(os.Stdout)

func next() string {
	return reader.next()
}

func nextInt64() int64 {
	i, err := strconv.ParseInt(reader.next(), 10, 64)
	if err != nil {
		panic(err)
	}
	return i
}

func nextInt() int {
	return int(nextInt64())
}

func nextLine() string {
	return reader.nextLine()
}

func out(a ...interface{}) {
	fmt.Fprintln(writer, a...)
}

func max64(x, y int64) int64 {
	if x > y {
		return x
	}
	return y
}

func max(x, y int) int {
	return int(max64(int64(x), int64(y)))
}

func min64(x, y int64) int64 {
	if x < y {
		return x
	}
	return y
}

func min(x, y int) int {
	return int(min64(int64(x), int64(y)))
}

func abs64(x int64) int64 {
	if x < 0 {
		return -x
	}
	return x
}

func abs(x int) int {
	return int(abs64(int64(x)))
}

func joinInt64s(a []int64, sep string) string {
	b := make([]string, len(a))
	for i, v := range a {
		b[i] = strconv.FormatInt(v, 10)
	}
	return strings.Join(b, sep)
}

func joinInts(a []int, sep string) string {
	b := make([]string, len(a))
	for i, v := range a {
		b[i] = strconv.Itoa(v)
	}
	return strings.Join(b, sep)
}

func divUp64(x, y int64) int64 {
	return (x + y - 1) / y
}

func divUp(x, y int) int {
	return int(divUp64(int64(x), int64(y)))
}

func gcd64(x, y int64) int64 {
	if x < y {
		x, y = y, x
	}
	for y != 0 {
		x, y = y, x%y
	}
	return x
}

func gcd(x, y int) int {
	return int(gcd64(int64(x), int64(y)))
}

func lcm64(x, y int64) int64 {
	return x * y / gcd64(x, y)
}

func lcm(x, y int) int {
	return int(lcm64(int64(x), int64(y)))
}

func pow64(x, y int64) int64 {
	return int64(math.Pow(float64(x), float64(y)))
}

func pow(x, y int) int {
	return int(pow64(int64(x), int64(y)))
}

func main() {
	solve()
	writer.Flush()
}

type queue struct {
	data [][]int
	from int
	to   int
}

func (q *queue) push(d []int) {
	q.data[q.to] = d
	q.to++
}

func (q *queue) pop() []int {
	d := q.data[q.from]
	q.from++
	return d
}

var dh = []int{0, 1}
var dw = []int{1, 0}

func solve() {
	H, W := nextInt(), nextInt()
	A := make([]string, H)
	for i := 0; i < H; i++ {
		A[i] = nextLine()
	}

	q := queue{make([][]int, H*W), 0, 0}

	if A[0][0] == '#' {
		q.push([]int{0, 0})
	}

	n := 0
	for i := 0; i < H; i++ {
		for j := 0; j < W; j++ {
			if A[i][j] == '#' {
				n++
			}
		}
	}

	reached := false

	for q.from != q.to {
		d := q.pop()
		n--
		if d[0] == H-1 && d[1] == W-1 {
			reached = true
			break
		}
		for i := 0; i < 2; i++ {
			nh := d[0] + dh[i]
			nw := d[1] + dw[i]
			if nh >= H || nw >= W {
				continue
			}
			if A[nh][nw] == '.' {
				continue
			}
			q.push([]int{nh, nw, d[0], d[1]})
		}
	}

	if n == 0 && reached {
		out("Possible")
	} else {
		out("Impossible")
	}
}