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.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Random;
import java.util.Scanner;

public class Main {
	public static void main(String[] $) throws IOException{
		int h=scan.nextInt();
		int w=scan.nextInt();
		char ch[][]=new char[h][w];
		for(int i=0;i<h;i++)ch[i]=scan.next().toCharArray();
		int cnt=0;
		for(int i=0;i<h;i++) {
			for(int j=0;j<w;j++) {
				if(ch[i][j]=='#')cnt++;
			}
		}
		if(cnt==h+w-1) {
			System.out.println("Possible");
		}
		else {
			System.out.println("Impossible");
		}
	}
	static FastScanner scan = new FastScanner();
	static Scanner scanner = new Scanner(System.in);
	static Random rand = new Random();
	static long mod = 1000000007;
	static double eps = 1.0E-14;
	static int big = Integer.MAX_VALUE;
	static double PI = 3.141592653589793;
	static long modlcm(long a, long b) {
		return a * b * modinv(GCD(a, b), mod);
	}
	static long GCD(long a, long b) {
		return b > 0 ? GCD(b, a % b) : a;
	}
	static long lcm(long a, long b) {
		return a * b / GCD(a, b);
	}
	static int min(int a, int b) {
		return a < b ? a : b;
	}
	static long factorial(int i) {
		return i == 1 ? 1 : i * factorial(i - 1);
	}
	static int max(int... i) {
		int x = i[0];
		for (int e : i)
			x = Math.max(x, e);
		return x;
	}
	static int min(int... i) {
		int x = i[0];
		for (int e : i)
			x = Math.min(x, e);
		return x;
	}
	static long gcd(long... i) {
		long x = i[0];
		for (long e : i)
			x = GCD(x, e);
		return x;
	}
	static long lmax(long... i) {
		long x = i[0];
		for (long e : i)
			x = Math.max(x, e);
		return x;
	}
	static long lmin(long... i) {
		long x = i[0];
		for (long e : i)
			x = Math.min(x, e);
		return x;
	}
	static long nCr(long n, long r, long m) {
		long ans = 1;
		for (long i = 0; i < r; i++) {
			ans *= (n - i);
			ans %= m;
		}
		for (long i = 0; i <= r; i++) {
			ans *= modinv(i, m);
			ans %= mod;
		}
		return ans;
	}
	static int lower_bound(int a[], int key) {
		int ok = a.length;
		int ng = -1;
		while (Math.abs(ok - ng) > 1) {
			int mid = (ok + ng) / 2;
			if (a[mid] >= key)
				ok = mid;
			else
				ng = mid;
		}
		return ok;
	}
	static int upper_bound(int a[], int key) {
		int ok = a.length;
		int ng = -1;
		while (Math.abs(ok - ng) > 1) {
			int mid = (ok + ng) / 2;
			if (a[mid] > key)
				ok = mid;
			else
				ng = mid;
		}
		return ok;
	}
	static boolean isPrime(long n) {
		if (n == 2)
			return true;
		if (n < 2 || n % 2 == 0)
			return false;
		double d = Math.sqrt(n);
		for (int i = 3; i <= d; i += 2)
			if (n % i == 0) {
				return false;
			}
		return true;
	}
	static int upper_division(int a, int b) {
		if (a % b == 0) {
			return a / b;
		} else {
			return a / b + 1;
		}
	}
	static long lupper_division(long a, long b) {
		if (a % b == 0) {
			return a / b;
		} else {
			return a / b + 1;
		}
	}
	static int[] setArray(int a) {
		int b[] = new int[a];
		for (int i = 0; i < a; i++) {
			b[i] = scan.nextInt();
		}
		return b;
	}
	static long[] lsetArray(int a) {
		long b[] = new long[a];
		for (int i = 0; i < a; i++) {
			b[i] = scan.nextLong();
		}
		return b;
	}
	static String reverse(String str) {
		char ch[] = new char[str.length()];
		char chch[] = str.toCharArray();
		int a = str.length();
		for (int i = 0; i < upper_division(a, 2); i++) {
			ch[i] = chch[ch.length - i - 1];
			ch[ch.length - 1 - i] = chch[i];
		}
		return String.valueOf(ch);
	}
	public static void printArray(int[] que) {
		for (int i = 0; i < que.length - 1; i++) {
			System.out.print(que[i] + " ");
		}
		System.out.println(que[que.length - 1]);
	}
	public static void lprintArray(long[] que) {
		for (int i = 0; i < que.length - 1; i++) {
			System.out.print(que[i] + " ");
		}
		System.out.println(que[que.length - 1]);
	}
	public static int[][] doublesort(int[][] a) {
		Arrays.sort(a, (x, y) -> Integer.compare(x[0], y[0]));
		return a;
	}
	public static long[][] ldoublesort(long[][] a) {
		Arrays.sort(a, (x, y) -> Long.compare(x[0], y[0]));
		return a;
	}
	static long modpow(long x, long n, long mo) {
		long sum = 1;
		while (n > 0) {
			if ((n & 1) == 1) {
				sum = sum * x % mo;
			}
			x = x * x % mo;
			n >>= 1;
		}
		return sum;
	}
	public static char[] revch(char ch[]) {
		char ret[] = new char[ch.length];
		for (int i = ch.length - 1, j = 0; i >= 0; i--, j++) {
			ret[j] = ch[i];
		}
		return ret;
	}
	public static int[] revint(int ch[]) {
		int ret[] = new int[ch.length];
		for (int i = ch.length - 1, j = 0; i >= 0; i--, j++) {
			ret[j] = ch[i];
		}
		return ret;
	}
	public static int[][] warshall_floyd(int v[][], int n) {
		for (int k = 0; k < n; k++)
			for (int i = 0; i < n; i++)
				for (int j = 0; j < n; j++)
					v[i][j] = min(v[i][j], v[i][k] + v[k][j]);
		return v;
	}
	public static long modinv(long a, long m) {
		long b = m, u = 1, v = 0;
		while (b != 0) {
			long t = a / b;
			a -= t * b;
			long x = a;
			a = b;
			b = x;
			u -= t * v;
			x = u;
			u = v;
			v = x;
		}
		u %= m;
		if (u < 0)
			u += m;
		return u;
	}
}
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;
	}
	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
		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 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();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
			throw new NumberFormatException();
		return (int) nl;
	}
	public double nextDouble() {
		return Double.parseDouble(next());
	}
	public char nextchar() {
		return next().charAt(0);
	}
}

class UnionFind {
	int Parent[];
	UnionFind(int n) {// Initialize by -1
		Parent = new int[n];
		Arrays.fill(Parent, -1);
	}
	int root(int A) {// In which tree is A?
		if (Parent[A] < 0)
			return A;
		return Parent[A] = root(Parent[A]);
	}
	int size(int A) {// size of tree which is include A
		return -Parent[root(A)];
	}
	boolean connect(int A, int B) {// Connect A and B
		A = root(A);
		B = root(B);
		if (A == B)
			return false;
		if (size(A) < size(B)) {
			int C = 0;
			C = B;
			B = A;
			A = C;
		} // SWAP
		Parent[A] += Parent[B];
		Parent[B] = A;
		return true;
	}
}

class Pair<T, E> {
	public T first;
	public E second;
	void set(T x, E y) {
		first = x;
		second = y;
	}
}

class Pint {
	public int first;
	public int second;
	Pint(int x, int y) {
		first = x;
		second = y;
	}
	void set(int x, int y) {
		first = x;
		second = y;
	}
}

class Tpair {
	public int first;
	public int second;
	public long third;
	Tpair(int x, int y, long z) {
		first = x;
		second = y;
		third = z;
	}
	void set(int x, int y, long z) {
		first = x;
		second = y;
		third = z;
	}
}