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"
	"math"
	"os"
	"strconv"
	"strings"
)

//Util
func nextStr() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func maxInt(a, b int) int {
	if a > b {
		return a
	} else {
		return b
	}
}

func minInt(a, b int) int {
	if a > b {
		return b
	} else {
		return a
	}
}

func absInt(a int) int {
	if a >= 0 {
		return a
	} else {
		return -a
	}
}

func absFloat64(a float64) float64 {
	if a >= 0 {
		return a
	} else {
		return -a
	}
}

func maxFloat64(a, b float64) float64 {
	if a > b {
		return a
	} else {
		return b
	}
}

func minFloat64(a, b float64) float64 {
	if a > b {
		return b
	} else {
		return a
	}
}

func str2Int(s string) int {
	n, _ := strconv.Atoi(s)
	return n
}

func reverse(s string) string {
	runes := []rune(s)
	for i, j := 0, len(runes)-1; i < j; i, j = i+1, j-1 {
		runes[i], runes[j] = runes[j], runes[i]
	}
	return string(runes)
}

func powInt(p, q int) int {
	return int(math.Pow(float64(p), float64(q)))
}

func isPrime(x int) bool {
	if x == 1 {
		return false
	}
	if x == 2 {
		return true
	}
	if x%2 == 0 {
		return false
	}

	b := true
	rootx := int(math.Sqrt(float64(x)))
	i := 3
	for i <= rootx {
		if x%i == 0 {
			b = false
			break
		}
		i += 2
	}
	return b
}

func PrimeFactors(n int) (pfs []int) {
	// Get the number of 2s that divide n
	for n%2 == 0 {
		pfs = append(pfs, 2)
		n = n / 2
	}

	// n must be odd at this point. so we can skip one element
	// (note i = i + 2)
	for i := 3; i*i <= n; i = i + 2 {
		// while i divides n, append i and divide n
		for n%i == 0 {
			pfs = append(pfs, i)
			n = n / i
		}
	}

	// This condition is to handle the case when n is a prime number
	// greater than 2
	if n > 2 {
		pfs = append(pfs, n)
	}

	return
}

func PrimeFactorsMap(n int) map[int]int {
	pfs := map[int]int{}
	// Get the number of 2s that divide n
	for n%2 == 0 {
		if _, ok := pfs[2]; ok {
			pfs[2]++
		} else {
			pfs[2] = 1
		}
		//pfs = append(pfs, 2)
		n = n / 2
	}

	// n must be odd at this point. so we can skip one element
	// (note i = i + 2)
	for i := 3; i*i <= n; i = i + 2 {
		// while i divides n, append i and divide n
		for n%i == 0 {
			if _, ok := pfs[i]; ok {
				pfs[i]++
			} else {
				pfs[i] = 1
			}
			n = n / i
		}
	}

	// This condition is to handle the case when n is a prime number
	// greater than 2
	if n > 2 {
		if _, ok := pfs[n]; ok {
			pfs[n]++
		} else {
			pfs[n] = 1
		}
	}

	return pfs
}

func sumInts(x []int) int {

	total := 0
	for _, v := range x {
		total += v
	}

	return total
}

//Main
const (
	initialBufSize = 10000
	maxBufSize     = 1000000
	mod            = 1e9 + 7
)

var (
	sc *bufio.Scanner = func() *bufio.Scanner {
		sc := bufio.NewScanner(os.Stdin)
		buf := make([]byte, initialBufSize)
		sc.Buffer(buf, maxBufSize)
		return sc
	}()
)

var N, K int

func main() {
	sc.Split(bufio.ScanWords)

	H, W, K := nextInt(), nextInt(), nextInt()
	c := make([]string, H)
	sum := 0
	for i := 0; i < H; i++ {
		c[i] = nextStr()
		sum += strings.Count(c[i], "#")
	}

	ans := 0
	for i := 0; i < (1 << uint(H)); i++ {
		for j := 0; j < (1 << uint(W)); j++ {
			s := "00000" + fmt.Sprintf("%b", i)
			t := "00000" + fmt.Sprintf("%b", j)
			done := make([][]int, H)
			for i := 0; i < H; i++ {
				done[i] = make([]int, W)
			}
			for a := 0; a < H; a++ {
				tmps := string(s[len(s)-1-a])
				if tmps != "1" {
					continue
				}
				for b := 0; b < W; b++ {
					if done[a][b] == 0 && string(c[a][b]) == "#" {
						done[a][b] = 1
					}
				}
			}
			for a := 0; a < W; a++ {
				tmpt := string(t[len(t)-1-a])
				if tmpt != "1" {
					continue
				}
				for b := 0; b < H; b++ {
					if done[b][a] == 0 && string(c[b][a]) == "#" {
						done[b][a] = 1
					}
				}
			}

			tmp := 0
			//fmt.Println(done, done[0][2])
			for i := 0; i < H; i++ {
				for j := 0; j < W; j++ {
					tmp += done[i][j]
				}
			}
			if sum-tmp == K {
				ans++
			}
		}
	}

	fmt.Println(ans)

}