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.BufferedWriter;


import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.math.BigDecimal;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Random;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;
public class Main {
	
	public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
        }
    class InputReader {


        private InputStream stream;

        private byte[] buf = new byte[1024];

        private int curChar;

        private int numChars;

        private SpaceCharFilter filter;
        

        public InputReader(InputStream stream) {

            this.stream = stream;

        }


        public int read() {

            if (numChars == -1)

                throw new InputMismatchException();

            if (curChar >= numChars) {

                curChar = 0;

                try {

                    numChars = stream.read(buf);

                } catch (IOException e) {

                    throw new InputMismatchException();

                }

                if (numChars <= 0)

                    return -1;

            }

            return buf[curChar++];

        }


        public int readInt() {

            int c = read();

            while (isSpaceChar(c))

                c = read();

            int sgn = 1;

            if (c == '-') {

                sgn = -1;

                c = read();

            }

            int res = 0;

            do {

                if (c < '0' || c > '9')

                    throw new InputMismatchException();

                res *= 10;

                res += c - '0';

                c = read();

            } while (!isSpaceChar(c));

            return res * sgn;

        }
        public long readLong() {

            int c = read();

            while (isSpaceChar(c))

                c = read();

            int sgn = 1;

            if (c == '-') {

                sgn = -1;

                c = read();

            }

            long res = 0;

            do {

                if (c < '0' || c > '9')

                    throw new InputMismatchException();

                res *= 10;

                res += c - '0';

                c = read();

            } while (!isSpaceChar(c));

            return res * sgn;

        }

        public String readString() {

            int c = read();

            while (isSpaceChar(c))

                c = read();

            StringBuilder res = new StringBuilder();

            do {

                res.appendCodePoint(c);

                c = read();

            } while (!isSpaceChar(c));

            return res.toString();

        }


        public boolean isSpaceChar(int c) {

            if (filter != null)

                return filter.isSpaceChar(c);

            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;

        }


        public String next() {

            return readString();

        }



    }


class OutputWriter {

        private final PrintWriter writer;


        public OutputWriter(OutputStream outputStream) {

            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));

        }


        public OutputWriter(Writer writer) {

            this.writer = new PrintWriter(writer);

        }


        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();

        }


        public void flush() {

            writer.flush();

        }


        }

    /**
     * @param args
     */

    InputReader in= new InputReader(System.in);
    OutputWriter out = new OutputWriter(System.out);
        StringTokenizer tok;
      
        public static void main(String[] args) throws IOException
        {
           new Main().run();
        }
        void run() throws IOException
        {
            
           solve();
           out.flush();
           tok=null;
        }
      

void  solve() throws IOException{
	int H=in.readInt();
	int W=in.readInt();
	int last_rock=0;
	int last_i=0;
	boolean sol=true;
	for (int i=0;i<H;++i){
		String s=in.readString();
		if (i==0 && s.charAt(0)!='#') {sol=false; break;}
		if (i==H-1 && s.charAt(W-1)!='#'){ sol=false; break;}
		for (int j=0;j<W;++j){
			if (s.charAt(j)=='#'){
				if (j<last_rock){
					sol=false;
					break;
				}else {
					if (j-last_rock>1){
						sol=false;
					}else if (i-last_i>1){
						sol=false;
					}else{
						last_rock=j;
						last_i=i;
					}
				}
					
			} if (!sol) break;
		}
	}
	if (sol) out.printLine("Possible");
	else out.printLine("Impossible");
}        
}