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.IOException;
import java.io.InputStream;
import java.io.PrintStream;
import java.util.NoSuchElementException;

public class Main {
	static FastScanner sc = new FastScanner();
	static PrintStream out = System.out;

	public static void main(String args[]) {
		int H = ni();
		int W = ni();
		int a[][] = new int[W][H];
		boolean isAns = false;

		for (int i=0;i<H;i++) {
			String s = next();
			for (int j=0;j<W;j++) {
				a[j][i] = (s.charAt(j) == '#') ? 1 : 0;
			}
		}

		int cnt = 0;
		for (int i=0;i<W;i++) {
			for (int j=0;j<H;j++) {
				if (a[i][j] == 1) {
					cnt++;
				}
			}
		}

		if (cnt == H + W - 1) {
			// search route
			isAns = search(a, W, H, 0, 0);
		}

		System.out.println(isAns ? "Possible" : "Impossible");
	}

	private static boolean search(int a[][], int W, int H, int x, int y) {
		if (x == W-1 && y == H-1) return true;

		boolean ret = false;
		if (x < W-1) {
			if (a[x+1][y] == 1) {
				ret |= search(a, W, H, x+1, y);
			}
		}
		if (y < H-1) {
			if (a[x][y+1] == 1) {
				ret |= search(a, W, H, x, y+1);
			}
		}

		return ret;
	}

	private static String next() {
		return sc.next();
	}

	private static int ni() {
		return sc.nextInt();
	}

	private static long nl() {
		return sc.nextLong();
	}

	private static int[] na(int n) {
		int[] a = new int[n];
		for(int i = 0;i < n;i++) a[i] = ni();
		return a;
	}

	private static long[] nal(int n) {
		long[] a = new long[n];
		for(int i = 0;i < n;i++) a[i] = ni();
		return a;
	}

	private static double nd() {
		return Double.parseDouble( next() );
	}
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
	public boolean hasNext() { skipUnprintable(); return hasNextByte();}
	public String next() {
		if (!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public int nextInt() {
		if (!hasNext()) throw new NoSuchElementException();
		int n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public long nextLong() {
		if (!hasNext()) throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
}