Problem:
Score : 200 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

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.

Sample Input 1

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

Sample Output 1

Possible

The matrix can be generated by a 7-move sequence: right, down, right, down, right, down, and right.

Sample Input 2

5 3
###
..#
###
#..
###

Sample Output 2

Impossible

Sample Input 3

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

Sample Output 3

Impossible

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <sstream>
#include <cmath>
#include <algorithm>
#include <utility>
#include <functional>
#include <iomanip>
#include <typeinfo>
#include <iterator>
#include <string>
#include <vector>
#include <queue>
#include <deque>
#include <tuple>
#include <map>
#include <set>
#include <numeric>
using namespace std;

#define all(container) container.begin(), container.end()
#define sortall(container) (sort(container.begin(), container.end()))
#define yn(cond) ((cond) ? (cout << "Yes" << endl) : (cout << "No" << endl))
#define YN(cond) ((cond) ? (cout << "YES" << endl) : (cout << "NO" << endl))
#define LLONG_MAX numeric_limits<long long>::max()
#define INT_MAX numeric_limits<int>::max()

typedef long long       ll;
typedef vector<int>     vi;
typedef vector<ll>      vll;
typedef vector<double>  vd;
typedef vector<bool>    vb;
typedef vector<string>  vs;
typedef vector<char>    vc;
typedef pair<int, int>  pii;
typedef pair<ll, ll>    pll;
typedef vector<pii>     vpii;
typedef vector<pll>     vpll;
typedef vector<vll>		vvll;
typedef vector<vi>		vvi;
typedef vector<vb>		vvb;
typedef vector<vs>		vvs;
typedef vector<vc>		vvc;

typedef struct edge_ {
	ll to;
	ll cost;
} edge;

typedef struct point_ {
	ll x, y;
	point_(ll x = 0, ll y = 0) : x(x), y(y) {}
} point;

constexpr double	PI = 3.14159265358979323846;
constexpr ll		INF = 1 << 15;
constexpr ll		MOD = (ll)1e9 + 7;
constexpr double	EPS = 1e-7;
constexpr int		dy4[4] = { 0, 1, 0, -1 };
constexpr int		dx4[4] = { 1, 0, -1, 0 };
constexpr int		dy8[8] = { 0, 1, 1, 1, 0, -1, -1, -1 };
constexpr int		dx8[8] = { 1, 1, 0, -1, -1, -1, 0, 1 };

template<typename T>
istream& operator >> (istream& is, vector<T>& vec) {
	for (T& x : vec) is >> x;
	return is;
}

template<typename T>
ostream& operator << (ostream& os, const vector<T>& vec) {
	for (const T& x : vec) os << x << " ";
	return os;
}

template<typename S, typename T>
istream& operator >> (istream& is, pair<S, T>& p) {
	is >> p.first >> p.second;
	return is;
}

istream& operator >> (istream& is, point& p) {
	is >> p.x >> p.y;
	return is;
}

template<typename S, typename T>
ostream& operator << (ostream& os, const pair<S, T>& p) {
	os << "{" << p.first << " " << p.second << "}";
	return os;
}

ostream& operator << (ostream& os, const point& p) {
	os << "(" << p.x << " " << p.y << ")";
	return os;
}

/******************************************************************************/
/**********************         Don't make WA !!         **********************/
/******************************************************************************/

template <typename T>
class mat2D {
private:
	vector<vector<T>> data;
public:
	mat2D(int rows, int cols) : data(vector<vector<T>>(rows, vector<T>(cols))) {}
	T operator () (int row, int col) { return data[row][col]; }

	friend istream& operator >> (istream& is, mat2D<T>& m) { return is >> m.data; }
	friend ostream& operator << (ostream& os, const mat2D<T>& m) {
		for (const vector<T>& row : m.data) os << row << endl;
		return os;
	}
};

int main()
{
	int H, W;
	cin >> H >> W;
	mat2D<char> A(H, W);
	cin >> A;

	for (int i = 0; i < H; i++) {
		for (int j = 0; j < W; j++) {
			if (A(i, j) == '.') continue;

			int count = 0, count1 = 0;
			if (i + 1 < H && A(i + 1, j) == '#') count++;
			if (j + 1 < W && A(i, j + 1) == '#') count++;
			if (i - 1 >= 0 && A(i - 1, j) == '.') count1++;
			if (j - 1 >= 0 && A(i, j - 1) == '.') count1++;

			if (i > 0 && j > 0 && count1 == 0) {
				cout << "Impossible" << endl;
				return 0;
			}

			if (count == 0 && i != H - 1 && j != W - 1) {
				cout << "Impossible" << endl;
				return 0;
			}

			if (count == 2) {
				cout << "Impossible" << endl;
				return 0;
			}
		}
	}

	cout << "Possible" << endl;

	return 0;
}