Problem:
Score : 300 points

Problem Statement

We have a grid of H rows and W columns of squares. The color of the square at the i-th row from the top and the j-th column from the left (1 \leq i \leq H, 1 \leq j \leq W) is given to you as a character c_{i,j}: the square is white if c_{i,j} is ., and black if c_{i,j} is #.

Consider doing the following operation:

Choose some number of rows (possibly zero), and some number of columns (possibly zero). Then, paint red all squares in the chosen rows and all squares in the chosen columns.

You are given a positive integer K. How many choices of rows and columns result in exactly K black squares remaining after the operation? Here, we consider two choices different when there is a row or column chosen in only one of those choices.

Constraints

1 \leq H, W \leq 6

1 \leq K \leq HW

c_{i,j} is . or #.

Input

Input is given from Standard Input in the following format:

H W K
c_{1,1}c_{1,2}...c_{1,W}
c_{2,1}c_{2,2}...c_{2,W}
:
c_{H,1}c_{H,2}...c_{H,W}

Output

Print an integer representing the number of choices of rows and columns satisfying the condition.

Sample Input 1

2 3 2
..#
###

Sample Output 1

5

Five choices below satisfy the condition.

The 1-st row and 1-st column

The 1-st row and 2-nd column

The 1-st row and 3-rd column

The 1-st and 2-nd column

The 3-rd column

Sample Input 2

2 3 4
..#
###

Sample Output 2

1

One choice, which is choosing nothing, satisfies the condition.

Sample Input 3

2 2 3
##
##

Sample Output 3

0

Sample Input 4

6 6 8
..##..
.#..#.
#....#
######
#....#
#....#

Sample Output 4

208

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.IO.Pipes;
using System.Linq;
using System.Numerics;
using System.Runtime.CompilerServices;

namespace AtCoderWorkspace
{
    public class Solver
    {
        int w;
        int h;
        public void Solve()
        {
            var cin = new Scanner();
            h = cin.nextInt();
            w = cin.nextInt();
            var k = cin.nextInt();
            var f = new int[h, w];
            for (int i = 0; i < h; i++)
            {
                var s = cin.next().ToArray();
                for (int j = 0; j < w; j++)
                {                    
                    var ii = s[j] == '.' ? 0 : 1;
                    f[i, j] = ii;
                }
            }

            // bit全探索
            var N = h;
            var M = w;
            var ans = 0;
            for (int bit = 0; bit < (1 << N); bit++)
            {
                for (int ibit = 0; ibit < (1 << M); ibit++)
                {
                    var tmpf = Copy(f);

                    var hbit = new bool[h];
                    for (int i = 0; i < N; i++)
                    {
                        if ((bit & (1 << i)) > 0) hbit[i] = true;
                        else hbit[i] = false;
                    }

                    var wbit = new bool[w];
                    for (int i = 0; i < M; i++)
                    {
                        if ((ibit & (1 << i)) > 0) wbit[i] = true;
                        else wbit[i] = false;
                    }

                    // 処理
                    // 行
                    for (int i = 0; i < N; i++)
                    {
                        if (hbit[i])
                        {
                            for (int j = 0; j < w; j++)
                            {
                                tmpf[i, j] = 2;
                            }
                        }
                    }

                    // 列
                    for (int i = 0; i < M; i++)
                    {
                        if (wbit[i])
                        {
                            for (int j = 0; j < h; j++)
                            {
                                tmpf[j, i] = 2;
                            }
                        }
                    }

                    var count = Count(tmpf);
                    if (count == k) ans++;
                }
                
            }

            Console.WriteLine(ans);
        }

        int[,] Copy(int[,] ff)
        {
            var ret = new int[h,w];
            for (int i = 0; i < h; i++)
            {
                for (int j = 0; j < w; j++)
                {
                    ret[i, j] = ff[i, j];
                }
            }
            return ret;
        }

        int Count(int[,] ff)
        {
            var ret = 0;
            for (int i = 0; i < h; i++)
            {
                for (int j = 0; j < w; j++)
                {
                    if (ff[i, j] == 1) ret++;
                }
            }
            return ret;
        }
    }

    class Scanner
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }

        public string next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return next();
            i = 0;
            return s[i++];
        }

        public int nextInt()
        {
            return int.Parse(next());
        }
        public int[] ArrayInt(int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextInt() + add;
            }
            return Array;
        }

        public int[] DPArrayInt(int N, int ex)
        {
            int[] Array = new int[N + ex];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextInt();
            }
            return Array;
        }

        public long nextLong()
        {
            return long.Parse(next());
        }

        public long[] ArrayLong(int N, long add = 0)
        {
            long[] Array = new long[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextLong() + add;
            }
            return Array;
        }

        public long[] DPArrayLong(int N, int ex)
        {
            long[] Array = new long[N + ex];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextLong();
            }
            return Array;
        }

        public double nextDouble()
        {
            return double.Parse(next());
        }


        public double[] ArrayDouble(int N, double add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = nextDouble() + add;
            }
            return Array;
        }
    }

    class Program
    {
        static void Main(string[] s) => new Solver().Solve();
    }
}