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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main {

	final static long MOD = 1000000007L;
	public static String[] Ws = null;
	public static int wsIndx = 0;
	public static BufferedReader in = null;
	public static ArrayList<int[]> list = new ArrayList<>();
	public static void main(String[] args) throws Exception {


		int H=nextInt();
		int W=nextInt();
		String[][] b = new String[H+2][W+2];
		Arrays.fill(b[0], ".");
		Arrays.fill(b[b.length-1], ".");
		for(int i=0;i<H;i++){
			b[i+1]=toStringArray("."+nextString()+".");
		}
		int x=1;
		int y=1;
		String ans = "Possible";
		//4方向の場合はx[i+around[n]][k+around[n+1]]n<4,8方向はn<8でループ
		int[] around = { -1, 0, 1, 0, -1, 1, 1, -1, -1 };
		while(x!=W||y!=H){
			b[y][x]=".";
//			print(b);
			boolean flg=false;
			for(int i=0;i<4;i++){
				if("#".equals(b[y+around[i+1]][x+around[i]])){
					if(i==0||i==3){
						System.out.println("Impossible");
						return;
					}
					if(flg==false){
						y=y+around[i+1];
						x=x+around[i];
						flg=true;
					}
				}
			}
			if(!flg){
				ans="Impossible";
				break;
			}
		}

		for(int i=0;i<b.length;i++){
			for(int k=0;k<b[i].length;k++){
				if("#".equals(b[i][k])){
					ans="Impossible";
				}
			}
		}

		System.out.println(ans);

	}

	public static void print(String[][] s){
		for(int i=0;i<s.length;i++){
			for(int k=0;k<s[i].length;k++){
				System.out.print(s[i][k]);
			}
			System.out.println();
		}
		System.out.println();
	}

	public static String[] toStringArray(String s) {
		String[] tmp = new String[s.length()];
		char[] c = s.toCharArray();
		for (int i = 0; i < tmp.length; i++) {
			tmp[i] = String.valueOf(c[i]);
		}
		return tmp;
	}

	public static String concatStringArray(String[] s){
		StringBuffer sb = new StringBuffer();
		for(String x:s){
			sb.append(x);
		}
		return sb.toString();
	}

	public static void check() throws Exception{
		if(in == null){
			in = new BufferedReader(new InputStreamReader(System.in));
		}
		if(Ws==null || Ws.length<=wsIndx){
			Ws = in.readLine().split(" ");
			wsIndx=0;
		}
	}
	public static int nextInt()throws Exception{
		check();
		return Integer.parseInt(Ws[wsIndx++]);
	}

	public static long nextLong()throws Exception{
		check();
		return Long.parseLong(Ws[wsIndx++]);
	}

	public static String nextString()throws Exception{
		check();
		return Ws[wsIndx++];
	}

	public static int[] nextInts()throws Exception{
		check();
		int[] tmp = new int[Ws.length];
		for(int i=0;i<tmp.length;i++){
			tmp[i]=Integer.parseInt(Ws[i]);
		}
		wsIndx=Ws.length;
		return tmp;
	}

	public static long[] nextLongs()throws Exception{
		check();
		long[] tmp = new long[Ws.length];
		for(int i=0;i<tmp.length;i++){
			tmp[i]=Long.parseLong(Ws[i]);
		}
		wsIndx=Ws.length;
		return tmp;
	}

	public static String[] nextStrings()throws Exception{
		check();
		wsIndx=Ws.length;
		return Ws;
	}


}