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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression, System.Linq.Expressions.UnaryExpression>;

class Program
{
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    const int M = 1000000007;
    const double eps = 1e-9;
    static int[] dd = { 0, 1, 0, -1, 0 };
    static void Main()
    {
        int h, w;
        sc.Multi(out h, out w);
        var a = new string[h];
        for (int i = 0; i < h; i++)
        {
            a[i] = sc.Str;
        }
        for (int i = 0; i < h; i++)
        {
            for (int j = 0; j < w; j++)
            {
                if (i == 0 && j == 0)
                {
                    if (a[i][j] == '.' || a[i + 1][j] == a[i][j + 1])
                    {
                        DBG("Impossible");
                        return;
                    }
                    continue;
                }
                if (i == h - 1 && j == w - 1)
                {
                    if (a[i][j] == '.' || a[i - 1][j] == a[i][j - 1])
                    {
                        DBG("Impossible");
                        return;
                    }
                    continue;
                }
                if (a[i][j] == '.') continue;

                if ((i < h - 1 && a[i + 1][j] == '#') == (j < w - 1 && a[i][j + 1] == '#') || (i > 0 && a[i - 1][j] == '#') == (j > 0 && a[i][j - 1] == '#'))
                {
                    DBG("Impossible");
                    return;
                }
            }
        }
        Prt("Possible");
        sw.Flush();
    }
    static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
    static T Max<T>(params T[] a) => a.Max();
    static T Min<T>(params T[] a) => a.Min();
    static void DBG<T>(params T[] a) => Console.WriteLine(string.Join(" ", a));
    static void DBG(params object[] a) => Console.WriteLine(string.Join(" ", a));
    static void Prt<T>(params T[] a) => sw.WriteLine(string.Join(" ", a));
    static void Prt(params object[] a) => sw.WriteLine(string.Join(" ", a));
}
class Score : IComparable
{
    int score, time;
    public int CompareTo(object obj)
    {
        var x = obj as Score;
        return this.score == x.score ? x.time.CompareTo(this.time) : this.score.CompareTo(x.score);
    }
}
static class ex
{
    public static void swap<T>(this IList<T> a, int i, int j) { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a)
    {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
public static class Operator<T>
{
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) => Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile();
    public static Func<T, T> Lambda(Unary op) => Expression.Lambda<Func<T, T>>(op(x), x).Compile();
}

class scanCHK : sc
{
    public static new string Str { get { var s = Console.ReadLine(); return s == s.Trim() ? s : ""; } }
}
class sc
{
    public static int Int => int.Parse(Str);
    public static long Long => long.Parse(Str);
    public static double Double => double.Parse(Str);
    public static string Str => Console.ReadLine().Trim();
    public static int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public static long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public static double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public static string[] StrArr => Str.Split();
    static bool eq<T, U>() => typeof(T).Equals(typeof(U));
    static T ct<T, U>(U inp) => (T)Convert.ChangeType(inp, typeof(T));
    static T cv<T>(string inp) => eq<T, int>() ? ct<T, int>(int.Parse(inp))
                         : eq<T, long>() ? ct<T, long>(long.Parse(inp))
                         : eq<T, double>() ? ct<T, double>(double.Parse(inp))
                         : eq<T, char>() ? ct<T, char>(inp[0])
                         : ct<T, string>(inp);
    public static void Multi<T>(out T a) => a = cv<T>(Str);
    public static void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public static void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public static void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public static void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
}
struct ModInt
{
    public static long Mod = 1000000007;
    long val;
    public ModInt(long v) { val = (v % Mod + Mod) % Mod; }

    public static implicit operator ModInt(long x) => new ModInt(x);
    public static explicit operator long(ModInt x) => x.val;

    public static ModInt operator+(ModInt x, ModInt y) => x.val + y.val;
    public static ModInt operator-(ModInt x, ModInt y) => x.val - y.val;
    public static ModInt operator*(ModInt x, ModInt y) => x.val * y.val;
    // must : gcd(y, Mod) == 1
    public static ModInt operator/(ModInt x, ModInt y) => x * ~y;
    // powmod(x, y, Mod);
    public static ModInt operator^(ModInt x, long y)
    {
        if (x.val == 0) return x;
        if (y == 0) return 1;
        var t = x ^ (y / 2);
        if ((y & 1) == 0) return t * t;
        return t * t * x;
    }

    public static ModInt operator-(ModInt x) => -(x.val);
    // inv(x) : x * inv(x) == 1
    // must : gcd(x, Mod) == 1
    public static ModInt operator~(ModInt x) => x ^ (Mod - 2);

    public override string ToString() => this.val.ToString();

    // public static bool operator==(ModInt x, ModInt y) => x.val == y.val;
    // public static bool operator!=(ModInt x, ModInt y) => x.val != y.val;
    // public override bool Equals(object obj) => obj != null && this.GetType() == obj.GetType() && this.val == ((ModInt)obj).val;
    // public override int GetHashCode() => (int)this.val;

}
class mymath
{
    public static long Mod = 1000000007;
    public static bool isprime(long a)
    {
        if (a < 2) return false;
        for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
        return true;
    }
    public static bool[] sieve(int n)
    {
        var p = new bool[n + 1];
        for (int i = 2; i <= n; i++) p[i] = true;
        for (int i = 2; i * i <= n; i++) if (p[i]) for (int j = i * i; j <= n; j += i) p[j] = false;
        return p;
    }
    public static List<int> getprimes(int n)
    {
        var prs = new List<int>();
        var p = sieve(n);
        for (int i = 2; i <= n; i++) if (p[i]) prs.Add(i);
        return prs;
    }
    public static long[][] E(int n)
    {
        var ret = new long[n][];
        for (int i = 0; i < n; i++) { ret[i] = new long[n]; ret[i][i] = 1; }
        return ret;
    }
    public static long[][] pow(long[][] A, long n)
    {
        if (n == 0) return E(A.Length);
        var t = pow(A, n / 2);
        if ((n & 1) == 0) return mul(t, t);
        return mul(mul(t, t), A);
    }
    public static long dot(long[] x, long[] y)
    {
        int n = x.Length;
        long ret = 0;
        for (int i = 0; i < n; i++) ret = (ret + x[i] * y[i]) % Mod;
        return ret;
    }
    public static long[][] trans(long[][] A)
    {
        int n = A[0].Length, m = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++)
        {
            ret[i] = new long[m];
            for (int j = 0; j < m; j++) ret[i][j] = A[j][i];
        }
        return ret;
    }
    public static long[] mul(long[][] A, long[] x)
    {
        int n = A.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = dot(x, A[i]);
        return ret;
    }
    public static long[][] mul(long[][] A, long[][] B)
    {
        int n = A.Length;
        var Bt = trans(B);
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = mul(Bt, A[i]);
        return ret;
    }
    public static long[] add(long[] x, long[] y)
    {
        int n = x.Length;
        var ret = new long[n];
        for (int i = 0; i < n; i++) ret[i] = (x[i] + y[i]) % Mod;
        return ret;
    }
    public static long[][] add(long[][] A, long[][] B)
    {
        int n = A.Length;
        var ret = new long[n][];
        for (int i = 0; i < n; i++) ret[i] = add(A[i], B[i]);
        return ret;
    }
    public static long pow(long a, long b)
    {
        if (a >= Mod) return pow(a % Mod, b);
        if (a == 0) return 0;
        if (b == 0) return 1;
        var t = pow(a, b / 2);
        if ((b & 1) == 0) return t * t % Mod;
        return t * t % Mod * a % Mod;
    }
    public static long inv(long a) => pow(a, Mod - 2);
    public static long gcd(long a, long b)
    {
        while (b > 0) { var t = a % b; a = b; b = t; }
        return a;
    }
    // a x + b y = gcd(a, b)
    public static long extgcd(long a, long b, out long x, out long y)
    {
        long g = a;
        x = 1;
        y = 0;
        if (b != 0)
        {
            g = extgcd(b, a % b, out y, out x);
            y -= a / b * x;
        }
        return g;
    }
    public static long lcm(long a, long b) => a * (b / gcd(a, b));
    public static long comb(int n, int r)
    {
        if (n < 0 || r < 0 || r > n) return 0;
        if (n - r < r) r = n - r;
        if (r == 0) return 1;
        if (r == 1) return n;
        int[] numer = new int[r], denom = new int[r];
        for (int k = 0; k < r; k++) { numer[k] = n - r + k + 1; denom[k] = k + 1; }
        for (int p = 2; p <= r; p++)
        {
            int piv = denom[p - 1];
            if (piv > 1)
            {
                int ofst = (n - r) % p;
                for (int k = p - 1; k < r; k += p) { numer[k - ofst] /= piv; denom[k] /= piv; }
            }
        }
        long ret = 1;
        for (int k = 0; k < r; k++) if (numer[k] > 1) ret = ret * numer[k] % Mod;
        return ret;
    }
}