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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var (
	H, W, K    int
	black, red [][]bool
)

func main() {
	defer writer.Flush()
	readVariables()
	var answer int
	for br := 0; br < 1<<H; br++ {
		for bc := 0; bc < 1<<W; bc++ {
			clearRed()
			for i := 0; i < H; i++ {
				if 1<<i&br > 0 {
					setRowRed(i)
				}
			}
			for j := 0; j < W; j++ {
				if 1<<j&bc > 0 {
					setColRed(j)
				}
			}
			k := count()
			if k == K {
				answer++
			}
		}
	}
	println(answer)
}

func count() int {
	var result int
	for i := 0; i < H; i++ {
		for j := 0; j < W; j++ {
			if black[i][j] && !red[i][j] {
				result++
			}
		}
	}
	return result
}

func setRowRed(i int) {
	for j := 0; j < W; j++ {
		red[i][j] = true
	}
}
func setColRed(j int) {
	for i := 0; i < H; i++ {
		red[i][j] = true
	}
}

func clearRed() {
	for i := 0; i < H; i++ {
		for j := 0; j < W; j++ {
			red[i][j] = false
		}
	}
}

func readVariables() {
	H, W, K = nextInt(), nextInt(), nextInt()
	black = make([][]bool, H)
	red = make([][]bool, H)
	for i := 0; i < H; i++ {
		black[i] = make([]bool, W)
		red[i] = make([]bool, W)
	}
	for i := 0; i < H; i++ {
		row := nextStr()
		for j := 0; j < W; j++ {
			black[i][j] = row[j] == '#'
		}
	}
}

/* Template */

var (
	scanner *bufio.Scanner
	writer  *bufio.Writer
)

func init() {
	Max := 1001001
	scanner = bufio.NewScanner(os.Stdin)
	scanner.Buffer(make([]byte, 0, Max), Max)
	scanner.Split(bufio.ScanWords)
	writer = bufio.NewWriterSize(os.Stdout, Max)
}

func println(a ...interface{}) {
	fmt.Fprintln(writer, a...)
}

func printf(format string, a ...interface{}) {
	fmt.Fprintf(writer, format, a...)
}

//nextInt converts next token from stdin and returns integer value.
//nextInt panics when conversion into an integer fails.
func nextInt() int {
	if !scanner.Scan() {
		panic("No more token.")
	}
	num, err := strconv.Atoi(scanner.Text())
	if err != nil {
		panic("nextInt(): cannot convert to int: " + scanner.Text())
	}
	return num
}

func nextStr() string {
	if !scanner.Scan() {
		panic("No more token.")
	}
	return scanner.Text()
}

// MinInt returns minimum argument
func MinInt(x, y int) int {
	if x < y {
		return x
	} else {
		return y
	}
}

//MaxInt returns maximum argument
func MaxInt(x, y int) int {
	if x < y {
		return y
	} else {
		return x
	}
}

//AbsInt returns |x| for x
func AbsInt(x int) int {
	if x < 0 {
		return -x
	}
	return x
}