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 <bits/stdc++.h>
#include <cmath>

//using namespace boost::multiprecision;
using namespace std;
typedef long long ll;
//typedef unsigned long long ll;
const double EPS = 1e-9;
#define rep(i, n) for (int i = 0; i < (n); ++i)
//#define rep(i, n) for (ll i = 0; i < (n); ++i)
//#define sz(x) ll(x.size())
typedef pair<int, int> P;
//typedef pair<ll, int> P;
//typedef pair<ll, ll> P;
//const double INF = 1e10;
const ll INF = LONG_LONG_MAX / 100;
//const ll INF = (1ll << 31) - 1;
//const ll INF = 1e15;
const ll MINF = LONG_LONG_MIN;
//const int INF = INT_MAX / 10;
#define cmin(x, y) x = min(x, y)
#define cmax(x, y) x = max(x, y)
//typedef pair<int, int> P;
//typedef pair<double, double> P;

bool contain(set<string> &s, string a) { return s.find(a) != s.end(); }

//ifstream myfile("C:\\Users\\riku\\Downloads\\0_00.txt");
//ofstream outfile("log.txt");
//outfile << setw(6) << setfill('0') << prefecture << setw(6) << setfill('0') << rank << endl;
// std::cout << std::bitset<8>(9);
const int mod = 1000000007;
typedef priority_queue<long long, vector<long long>, greater<long long> > PQ_ASK;


int main() {
    int h, w;
    cin >> h >> w;
    vector<vector<char>> board(h, vector<char>(w));
    rep(y, h) rep(x, w) cin >> board[y][x];

    auto can = [&](int y, int x) {
        if (y == h) return false;
        if (x == w) return false;
        if (board[y][x] == '.') return false;
        return true;
    };
    auto set = [&](int y, int x) {
        if (!can(y, x)) return;
        board[y][x] = 'o';
    };

    board[0][0] = 'o';
    rep(y, h)rep(x, w) {
            if (board[y][x] == 'o') {
                if (can(y + 1, x)) {
                    set(y + 1, x);
                } else if (can(y, x + 1)) {
                    set(y, x + 1);
                }
            }
        }


    rep(y, h)rep(x, w) {
            if (board[y][x] == '#') {
                cout << "Impossible" << endl;
                return 0;
            }
        }

    cout << (board.back().back() == 'o' ? "Possible" : "Impossible") << endl;
}