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:
/* Template */

/*
 * Contest: AGC007
 * Author : shu
 * Date   : 2016/11/16
 */

/* Import */
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.InputMismatchException;

public class Main {
	public static final int A = 1;
	public static final int B = 2;
	public static final int C = 3;
	public static final int D = 4;
	public static final int E = 5;
	public static final int F = 6;

	public static final int PROBREM_NUMBER = A;

	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		Problem probrem = new Problem();
		probrem.solve(PROBREM_NUMBER, in, out);
		out.close();
	}
}

class Problem {
	public void solve(int probremNumber, InputReader in, OutputWriter out) {
		switch (probremNumber) {
		case Main.A:
			A(in, out);
			break;
		case Main.B:
			B(in, out);
			break;
		case Main.C:
			C(in, out);
			break;
		case Main.D:
			D(in, out);
			break;
		case Main.E:
			E(in, out);
			break;
		case Main.F:
			F(in, out);
			break;
		default:
			out.print("PROBREM SELECTION ERROR");
		}
	}

	public void A(InputReader in, OutputWriter out) {
		int h = in.nextInt();
		int w = in.nextInt();
		
		int[][] a = new int[h+2][w+2];
		boolean flag = true;
		int x = 1;
		int y = 1;
		
		for (int i=1; i<=h; i++) {
			for (int j=1; j<=w; j++) {
				if (in.readSkipSpace() == '#') {
					a[i][j] = 1;
				} else {
					a[i][j] = 0;
				}
			}
		}
		
		while (flag) {
			if (a[x+1][y] == 1) {
				if (a[x][y+1]==1 || a[x+1][y-1]==1) {
					flag = false;
				}
				x++;
			} else {
				if (a[x][y+1]==1) {
					if (a[x-1][y+1]==1) {
						flag = false;
					}
					y++;
				}
			}
			
			if (x==h && y==w && flag==true) {
				break;
			}
		}
		
		if (flag==true) {
			out.printLine("Possible");
		} else {
			out.printLine("Impossible");
		}
	}

	public void B(InputReader in, OutputWriter out) {

	}

	public void C(InputReader in, OutputWriter out) {

	}

	public void D(InputReader in, OutputWriter out) {

	}

	public void E(InputReader in, OutputWriter out) {

	}

	public void F(InputReader in, OutputWriter out) {

	}
}


class InputReader {
    private InputStream stream;
    private byte[] buffer = new byte[10000];
    private int cur;
    private int count;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public static boolean isSpace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public int read() {
        if (count == -1) {
            throw new InputMismatchException();
        }
        try {
            if (cur >= count) {
                cur = 0;
                count = stream.read(buffer);
                if (count <= 0)
                    return -1;
            }
        } catch (IOException e) {
            throw new InputMismatchException();
        }
        return buffer[cur++];
    }

    public int readSkipSpace() {
        int c;
        do {
            c = read();
        } while (isSpace(c));
        return c;
    }

    public int nextInt() {
        int sgn = 1;
        int c = readSkipSpace();
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9') {
                throw new InputMismatchException();
            }
            res = res * 10 + c - '0';
            c = read();
        } while (!isSpace(c));
        res *= sgn;
        return res;
    }

}

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0) {
                writer.print(' ');
            }
            writer.print(objects[i]);
        }
    }

    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }
}