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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;

using static System.Console;
using static AtCoder.Util;
using static AtCoder.Cin;
using static System.Math;
using static AtCoder.MyMath;

namespace AtCoder {
    class Program {
        static void Main() {
            var h = ReadInt();
            var w = ReadInt();
            var a = ReadString(h);

            var current = 0;
            foreach (var l in a) {
                var b = l.Take(current - 1).All(x => x == '.');
                b &= l[current] == '#';
                current += l.Skip(current).TakeWhile(x => x == '#').Count() - 1;
                b &= l.Skip(current + 1).All(x => x == '.');
                if (!b) {
                    WriteLine("Impossible");
                    return;
                }
            }
            WriteLine("Possible");
        }

    }
}

/* ***************** Following Contents are my common library ******** */

namespace AtCoder {

    static class MyMath {
        public static long ToNearestInt(this double d) {
            var l = (long) Math.Floor(d);
            var r = l + 1;
            return r - d < d - l ? r : l;
        }

        public static long Factorial(this long n) => Range(1, n).Aggregate(1L, Multiply);
        public static long nPr(int n, int r) => r < 0 || r > n ? 0 : FromTo(n - r + 1, n).Select(x =>(long) x).Aggregate(1L, Multiply);
        public static long nCr(int n, int r) => nPr(n, r) / Factorial(r);

        public static long Inc(long i) => i + 1;
        public static long Dec(long i) => i - 1;
        public static long Plus(long i, long j) => i + j;
        public static Func<long, long> Plus(long j) => i => i + j;
        public static long Minus(long i, long j) => i - j;
        public static Func<long, long> Minus(long j) => i => i - j;
        public static long Multiply(long i, long j) => i * j;
        public static Func<long, long> Multiply(long j) => i => i * j;
        public static long Divide(long i, long j) => j / j;
        public static Func<long, long> Divide(long j) => i => i * j;
        public static long Mod(long i, long j) => i % j;
        public static Func<long, long> Mod(long j) => i => i % j;

        public static long Max(params long[] ns) => ns.Max();

        public static bool InRange(this long x, long min, long max) => min <= x && x <= max;
        public static bool IsEven(this int x) => x % 2 == 0;
        public static bool IsOdd(this int x) => x % 2 != 1;
        public static bool IsEven(this long x) => x % 2 == 0;
        public static bool IsOdd(this long x) => x % 2 != 1;
    }

    static class Util {

        public static string Show(this IEnumerable<char> source) => new string(source.ToArray());

        public static IEnumerable<int> ToDigits(this long n) =>
            n.ToString().Select(x => x.ToInt());

        public static IEnumerable<int> Factors(this int n) {
            for (int i = 1; i <= n; i++)
                if (n % i == 0) yield return i;
        }

        public static IEnumerable<int> Natural() {
            for (int i = 0;; i++) yield return i;
        }
        public static IEnumerable<int> Positive() => Natural().Skip(1);

        public static long Pow(long i, long exp) =>(exp == 0) ? 1 : i * Pow(i, exp - 1);
        public static HashSet<T> ToHashSet<T>(this IEnumerable<T> source) => new HashSet<T>(source);

        public static MultiSet<T> ToMultiSet<T>(this IEnumerable<T> t) => new MultiSet<T>(t);

        public static int Max(this int i, int j) => i > j ? i : j;

        public static bool IsPalindrome(string s) {
            for (int i = 0; i < s.Length / 2; i++) {
                if (s[i] != s[s.Length - 1 - i]) return false;
            }
            return true;
        }
        public readonly static VectorInt2[] Dir8 = {
            new VectorInt2(-1, -1),
            new VectorInt2(-1, 0),
            new VectorInt2(-1, 1),
            new VectorInt2(0, -1),
            new VectorInt2(0, 1),
            new VectorInt2(1, -1),
            new VectorInt2(1, 0),
            new VectorInt2(1, 1)
        };

        public const long MODCONST = 1000000007;

        public static T debug<T>(this T value) {
            Console.Error.WriteLine($"debug:{value}");
            return value;
        }

        public static T Id<T>(T t) => t;
        public static long ToLong(this String s) => long.Parse(s);
        public static long ToLong(this char c) => c - '0';
        public static int ToInt(this String s) => int.Parse(s);
        public static int ToInt(this char c) => c - '0';
        public static void Times(this int n, Action action) {
            for (int i = 0; i < n; i++) action();
        }
        public static void Times(this long n, Action action) {
            for (long i = 0; i < n; i++) action();
        }

        public static IEnumerable<T> Times<T>(this int n, Func<T> func) {
            for (long i = 0; i < n; i++) yield return func();
        }
        public static IEnumerable<T> Times<T>(this long n, Func<T> func) {
            for (long i = 0; i < n; i++) yield return func();
        }

        public static Func<S, U> Then<S, T, U>(this Func<S, T> f, Func<T, U> g) => x => g(f(x));
        public static Func<S, U> Compose<S, T, U>(this Func<T, U> f, Func<S, T> g) => x => f(g(x));

        public static void Call<T>(this T t, Action<T> action) => action(t);
        public static bool In<T>(this T t, IEnumerable<T> range) =>
            range.Contains(t);
        public static void WriteLine<T>(this T t) => Console.WriteLine(t);
        public static T Call<S, T>(this S s, Func<S, T> func) => func(s);
        public static void Each<T>(this IEnumerable<T> e, Action<T> action) {
            foreach (var v in e) action(v);
        }

        public static long Prod(this IEnumerable<long> source) => source.Aggregate(Multiply);

        public static IEnumerable<int> FromTo(int a, int b) => Range(a, Max(b - a + 1, 0));
        public static IEnumerable<T> Repeat<T>(T t) {
            while (true) yield return t;
        }
        public static IEnumerable<T> Replicate<T>(int n, T t) => Repeat(t).Take(n);

        public static IEnumerable<T> Cycle<T>(this IEnumerable<T> e) {
            while (true)
                foreach (var v in e) yield return v;
        }

        public static IEnumerable<T> Scan<S, T>(this IEnumerable<S> source, T init, Func<T, S, T> accumulator) {
            var result = init;
            foreach (var item in source) {
                result = accumulator(result, item);
                yield return result;
            }
        }

        public static T[] ToArray<T>(params T[] ns) => ns;
        public static List<T> ToList<T>(params T[] ns) => ns.ToList();

        public static IEnumerable<T> Scan0<S, T>(this IEnumerable<S> source, T init, Func<T, S, T> accumulator) {
            yield return init;
            foreach (var item in Scan(source, init, accumulator)) yield return item;
        }

        public static IEnumerable<List<T>> Buffer<T>(this IEnumerable<T> source, int length) {
            while (source.Any()) {
                yield return source.Take(length).ToList();
                source = source.Skip(length);
            }
        }

        public static VectorInt2 ReadVectorInt2() =>
            new VectorInt2(ReadInt(), ReadInt());

        public static string ReplaceX(this string input, string pattern, string replace) =>
            Regex.Replace(input, pattern, replace);

        public static IEnumerable<int> Range(int i, int j) => Enumerable.Range(i, j);
        public static IEnumerable<long> Range(long i, long j) {
            for (long k = i; k < i + j; k++) yield return k;

        }
        public static void Swap<T>(this IList<T> enumerable, int i, int j) {
            var buf = enumerable[i];
            enumerable[i] = enumerable[j];
            enumerable[j] = buf;

        }
        public static void ReverseRange<T>(this IList<T> enumerable, int i, int j) {
            int half = (j - i) / 2;
            for (int k = 0; k <= half; k++) enumerable.Swap(i + k, j - k);
        }

        public static bool isEmpty<T>(this IEnumerable<T> enumerable) => !enumerable.Any();
    }

    static class Cin {
        private static Queue<string> tokens;
        static Cin() {
        string line;
        tokens = new Queue<string>();
        while ((line = Console.ReadLine()) != null) {
        foreach (var token in line.Split(' ')) {
        tokens.Enqueue(token);
                }
            }
        }

        static public int ReadInt() => int.Parse(tokens.Dequeue());
        static public List<int> ReadInt(long n) {
            var list = new List<int>();
            n.Times(() => list.Add(ReadInt()));
            return list;
        }
        static public long ReadLong() => long.Parse(tokens.Dequeue());
        static public List<long> ReadLong(long n) {
            var list = new List<long>();
            n.Times(() => list.Add(ReadLong()));
            return list;
        }
        static public string ReadString() => tokens.Dequeue();
        static public List<string> ReadString(long n) {
            var list = new List<string>();
            n.Times(() => list.Add(ReadString()));
            return list;
        }

        static public void SayYesNo(this bool b) =>(b ? "Yes" : "No").WriteLine();
    }

    struct VectorInt2 {
        public int X { get; set; }
        public int Y { get; set; }

        public VectorInt2(int x, int y) {
            X = x;
            Y = y;
        }

        static public VectorInt2 operator +(VectorInt2 v1, VectorInt2 v2) =>
            new VectorInt2(v1.X + v2.X, v1.Y + v2.Y);
        static public VectorInt2 operator -(VectorInt2 v1, VectorInt2 v2) =>
            new VectorInt2(v1.X - v2.X, v1.Y - v2.Y);
        static public VectorInt2 operator *(VectorInt2 v1, VectorInt2 v2) =>
            new VectorInt2(v1.X * v2.X, v1.Y * v2.Y);
        static public VectorInt2 operator *(VectorInt2 v1, int i) =>
            new VectorInt2(v1.X * i, v1.Y * i);
        static public VectorInt2 operator *(int i, VectorInt2 v2) =>
            new VectorInt2(i * v2.X, i * v2.Y);
        static public VectorInt2 operator /(VectorInt2 v1, int i) =>
            new VectorInt2(v1.X / i, v1.Y / i);
    }

    class Maxer<T> where T : IComparable<T> {
        public T Value;

        public Maxer(T t) {
            Value = t;
        }

        public void Max(T other) {
            if (Value.CompareTo(other) < 0) Value = other;
        }
    }

    class MultiSet<T> : IEnumerable<KeyValuePair<T, int>> {
        Dictionary<T, int> dictionary = new Dictionary<T, int>();

        public MultiSet(IEnumerable<T> data) {
            foreach (var datum in data) {
                if (dictionary.ContainsKey(datum)) {
                    dictionary[datum]++;
                } else {
                    dictionary[datum] = 1;
                }
            }
        }

        public int this [T key] {
            get {
                return dictionary.ContainsKey(key) ? dictionary[key] : 0;
            }
        }
        public MultiSet() {}

        public static MultiSet<S> ToMultiSet<S>(IEnumerable<S> source) => new MultiSet<S>(source);

        public Dictionary<T, int> AsDict() => dictionary;

        public IEnumerator<KeyValuePair<T, int>> GetEnumerator() => dictionary.GetEnumerator();
        IEnumerator IEnumerable.GetEnumerator() => this.GetEnumerator();
    }
}