Problem: 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`.

Examples

Input

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


Output

Possible


Input

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


Output

Possible


Input

5 3

..#

..


Output

Impossible


Input

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


Output

Impossible

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Queue;
import java.util.Set;

public class Main {
	final int _intMax = Integer.MAX_VALUE; //=2147483647>10^9
	final long _longMax = Long.MAX_VALUE; //=9223372036854775807L>10^18
	static boolean bElapsed = false;
	StringBuilder sb = new StringBuilder();
	List<String> list = new ArrayList<>();
	Set<String> set = new HashSet<>();
	Queue<String> queue = new ArrayDeque<>();
	Deque<String> stack = new ArrayDeque<>();
	boolean[][] map;
	int h;
	int w;

	void solve() {
		int[] ia = readNums();
		h = ia[0];
		w = ia[1];
		map = new boolean[h+2][w+2];
		for (int i=1; i<=h; i++) {
			String line = readLine();
			for (int j=1; j<=w; j++) {
				char ch = line.charAt(j-1);
				if (ch == '#') map[i][j] = true;
			}
		}
		search(1, 1);
		for (int y=1; y<=h; y++) {
			for (int x=1; x<=w; x++) {
				if (map[y][x]) {
					pln("Impossible");
					return;
				}
			}
		}
		pln("Possible");
	}
	
	void search(int x, int y) {
		while (true) {
			if (map[y][x]) map[y][x] = false;
			if (x == w && y == h) return;
			if (map[y][x+1]) {
				x++;
			} else if (map[y+1][x]) {
				y++;
			} else {
				return;
			}
		}
	}

	class Point {
		int x;
		int y;
		public Point(int x, int y) {
			this.x = x;
			this.y = y;
		}
		public boolean equals(Object o) {
			if (o instanceof Point) {
				Point that = (Point)o;
				return (x == that.x) && (y == that.y);
			}
			return false;
		}
		public int hashCode() {
			return x + (y << 16);
		}
		public String toString() {
			return "(" + x + ", " + y + ")";
		}
	}
	class Info implements Comparable<Info> {
		int idx;
		int val;
		public Info(int idx, int val) {
			this.idx = idx;
			this.val = val;
		}
		public int compareTo(Info o) {
			return idx - o.idx;
		}
		public boolean equals(Object o) {
			if (o instanceof Info) {
				Info that = (Info)o;
				return 0 == compareTo(that);
			}
			return false;
		}
		public int hashCode() {
			return idx + (val << 16);
		}
		public String toString() {
			return "(" + idx + ", " + val + ")";
		}
	}
	class InfoComp implements Comparator<Info> {
		public int compare(Info o1, Info o2) {
			return o1.val - o2.val;
		}
	}
	int pint(String s) {
		return Integer.parseInt(s);
	}
	String readLine() {
		try {
			_line = _in.readLine();
			return _line;
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
	}
	int readNum() {
		readLine();
		return pint(_line);
	}
	String[] readFields() {
		readLine();
		_flds = _line.split(" ");
		return _flds;
	}
	int[] readNums() {
		readFields();
		_nums = new int[_flds.length];
		for (int i=0; i<_flds.length; i++) {
			_nums[i] = pint(_flds[i]);
		}
		return _nums;
	}
	void p(char c) {
		_out.print(c);
	}
	void pln(char c) {
		_out.println(c);
	}
	void p(double d) {
		_out.print(d);
	}
	void pln(double d) {
		_out.println(d);
	}
	void p(long l) {
		_out.print(l);
	}
	void pln(long l) {
		_out.println(l);
	}
	void p(String s) {
		_out.print(s);
	}
	void pln(String s) {
		_out.println(s);
	}
	String _line;
	String[] _flds;
	int[] _nums;
	static BufferedReader _in;
	static PrintWriter _out;
	public static void main(String[] args) {
		long start = System.currentTimeMillis();
		_in = new BufferedReader(new InputStreamReader(System.in));
		_out = new PrintWriter(System.out);
		new Main().solve();
		_out.flush();
		long end = System.currentTimeMillis();
		if (bElapsed) {
			System.err.println((end-start) + "ms");
		}
	}
}