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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CHAndV solver = new CHAndV();
        solver.solve(1, in, out);
        out.close();
    }

    static class CHAndV {
        ArrayList<ArrayList<Integer>> psr;
        ArrayList<ArrayList<Integer>> psc;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int ntc = 1;
//        ntc = in.nextInt();
            while ((ntc--) > 0) {
                int n = in.nextInt();
                int m = in.nextInt();
                int k = in.nextInt();
                boolean[][] omat = new boolean[n][m];
                for (int i = 0; i < n; i++) {
                    for (int j = 0; j < m; j++) {
                        omat[i][j] = in.nextCharacter() == '#';
                    }
                }
                int ans = 0;
                psr = new ArrayList<>();
                psc = new ArrayList<>();
                ArrayList<Integer> sub = new ArrayList<>();
                getPowerSet(psr, sub, n - 1);
                sub = new ArrayList<>();
                getPowerSet(psc, sub, m - 1);
//            debug(psr);
//            debug(psc);
                for (ArrayList<Integer> subr : psr) {
                    for (ArrayList<Integer> subc : psc) {
                        boolean[][] mat = new boolean[n][m];
                        for (int i = 0; i < n; i++) {
                            for (int j = 0; j < m; j++) {
                                mat[i][j] = omat[i][j];
                            }
                        }
                        for (int r : subr) {
                            for (int j = 0; j < m; j++) {
                                mat[r][j] = false;
                            }
                        }
                        for (int c : subc) {
                            for (int j = 0; j < n; j++) {
                                mat[j][c] = false;
                            }
                        }
                        int count = 0;
                        for (int i = 0; i < n; i++) {
                            for (int j = 0; j < m; j++) {
                                if (mat[i][j]) {
                                    count++;
                                }
                            }
                        }
                        if (count == k) {
                            ans++;
                        }
                    }
                }
                out.println(ans);
            }
        }

        public void getPowerSet(ArrayList<ArrayList<Integer>> ps, ArrayList<Integer> sub, int n) {
            if (n <= -1) {
                ps.add(new ArrayList<>(sub));
                return;
            }
            getPowerSet(ps, sub, n - 1);
            sub.add(n);
            getPowerSet(ps, sub, n - 1);
            sub.remove(sub.size() - 1);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public char nextCharacter() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            return (char) c;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(long i) {
            writer.println(i);
        }

    }
}