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"
)

var mod = 1000000007
var inf = 1000000007

func main() {
	r := bufio.NewReader(os.Stdin)
	var h, w, k int
	fmt.Fscan(r, &h)
	fmt.Fscan(r, &w)
	fmt.Fscan(r, &k)
	grid := make([]string, h)
	knum := 0
	for i := 0; i < h; i++ {
		fmt.Fscan(r, &grid[i])
		for j := 0; j < w; j++ {
			if grid[i][j] == '#' {
				knum++
			}
		}
	}

	ans := 0
	for wi := 0; wi < (1 << uint(h)); wi++ {
		for wj := 0; wj < (1 << uint(w)); wj++ {
			count := 0

			for i := 0; i < h; i++ {
				if wi>>uint(i)&1 == 1 {
					continue
				}
				for j := 0; j < w; j++ {
					if wj>>uint(j)&1 == 1 {
						continue
					}

					if grid[i][j] == '#' {
						count++
					}
				}
			}
			if count == k {
				ans++
			}
		}

	}
	fmt.Println(ans)

}

// permutations
func permutations(arr []int) [][]int {
	var helper func([]int, int)
	res := [][]int{}

	helper = func(arr []int, n int) {
		if n == 1 {
			tmp := make([]int, len(arr))
			copy(tmp, arr)
			res = append(res, tmp)
		} else {
			for i := 0; i < n; i++ {
				helper(arr, n-1)
				if n%2 == 1 {
					tmp := arr[i]
					arr[i] = arr[n-1]
					arr[n-1] = tmp
				} else {
					tmp := arr[0]
					arr[0] = arr[n-1]
					arr[n-1] = tmp
				}
			}
		}
	}
	helper(arr, len(arr))
	return res
}

// Union-Find
type unionFind struct {
	d []int
}

func newUnionFind(n int) *unionFind {
	uf := new(unionFind)
	uf.d = make([]int, n)
	for i := 0; i < n; i++ {
		uf.d[i] = -1
	}
	return uf
}

func (uf *unionFind) find(x int) int {
	if uf.d[x] < 0 {
		return x
	}
	uf.d[x] = uf.find(uf.d[x])
	return uf.d[x]
}

func (uf *unionFind) unite(x, y int) bool {
	rootX := uf.find(x)
	rootY := uf.find(y)
	if rootX == rootY {
		return false
	}

	if uf.d[rootX] < uf.d[rootY] {
		uf.d[rootX] += uf.d[rootY]
		uf.d[rootY] = rootX
	} else {
		uf.d[rootY] += uf.d[rootX]
		uf.d[rootX] = rootY
	}

	return true
}

func (uf *unionFind) same(x, y int) bool {
	return uf.find(x) == uf.find(y)
}

func (uf *unionFind) size(x int) int {
	return -uf.d[uf.find(x)]
}

// mod
func modpow(a, n, mod int) int {
	res := 1
	for n > 0 {
		if n%2 != 0 {
			res = res * a % mod
		}
		a = a * a % mod
		n = n / 2
	}
	return res
}

func modinv(n, mod int) int {
	return modpow(n, mod-2, mod)
}

func modcomb(n, a, mod int) int {
	x := 1
	y := 1
	for i := 0; i < a; i++ {
		x = x * (n - i)
		x %= mod
		y = y * (i + 1)
		y %= mod
	}
	return x * modpow(y, mod-2, mod) % mod
}

func modfactorial(n, mod int) int {
	result := 1
	for i := 1; i <= n; i++ {
		result = (result * i) % mod
	}
	return result
}

// Combination ...
type Combination struct {
	facts, invs []int
	mod         int
}

// NewCombination ...
func NewCombination(n, mod int) Combination {
	return Combination{
		facts: make([]int, n+1),
		invs:  make([]int, n+1),
		mod:   mod,
	}
}

func (cmb *Combination) calc(n, k int) int {
	ret := cmb.facts[n] * cmb.invs[k]
	ret %= cmb.mod
	ret = ret * cmb.invs[n-k]
	ret %= cmb.mod
	return ret
}

func (cmb *Combination) init(n int) {
	cmb.facts[0] = 1
	// 階乗を算出
	for i := 1; i <= n; i++ {
		cmb.facts[i] = cmb.facts[i-1] * i % cmb.mod
	}
	// 逆元を算出
	cmb.invs[n] = modinv(cmb.facts[n], cmb.mod)
	for i := n - 1; i >= 0; i-- {
		cmb.invs[i] = cmb.invs[i+1] * (i + 1) % cmb.mod
	}
}

// Utility
func min(x, y int) int {
	if x < y {
		return x
	}
	return y
}

func max(x, y int) int {
	if x > y {
		return x
	}
	return y
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

func primeFactor(x int) map[int]int {
	res := make(map[int]int)
	for i := 2; i*i <= x; i++ {
		for x%i == 0 {
			res[i]++
			x = x / i
		}
	}
	if x != 1 {
		res[x] = 1
	}
	return res
}

func divisor(x int) []int {
	res := make([]int, 0)
	for i := 1; i*i <= x; i++ {
		if x%i == 0 {
			res = append(res, i)
			if i != x/i {
				res = append(res, x/i)
			}
		}
	}
	return res
}

func gcd(x, y int) int {
	if y == 0 {
		return x
	}
	return gcd(y, x%y)
}

func lcm(x, y int) int {
	return x / gcd(x, y) * y
}

func reverseString(s string) string {
	r := []rune(s)
	for i, j := 0, len(r)-1; i < len(r)/2; i, j = i+1, j-1 {
		r[i], r[j] = r[j], r[i]
	}
	return string(r)
}

func pow(a, n int) int {
	ret := 1
	for i := 1; i <= n; i++ {
		ret *= a
	}
	return ret
}

// Queue ...
type Queue []int

// pop ...
func (q *Queue) empty() bool {
	return len(*q) == 0
}

// push ...
func (q *Queue) push(i int) {
	*q = append(*q, i)
}

// pop ...
func (q *Queue) pop() (int, bool) {
	if q.empty() {
		return 0, false
	} else {
		res := (*q)[0]
		*q = (*q)[1:]
		return res, true
	}
}

// Stack ...
type Stack []int

// pop ...
func (s *Stack) empty() bool {
	return len(*s) == 0
}

// push ...
func (s *Stack) push(i int) {
	*s = append(*s, i)
}

// pop ...
func (s *Stack) pop() (int, bool) {
	if s.empty() {
		return 0, false
	} else {
		index := len(*s) - 1
		res := (*s)[index]
		*s = (*s)[:index]
		return res, true
	}
}

// priority_queue
type intHeap []int

func (h intHeap) Len() int           { return len(h) }
func (h intHeap) Less(i, j int) bool { return h[i] > h[j] }
func (h intHeap) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }
func (h *intHeap) Push(x interface{}) {
	*h = append(*h, x.(int))
}
func (h *intHeap) Pop() interface{} {
	old := *h
	n := len(old)
	x := old[n-1]
	*h = old[0 : n-1]
	return x
}

// sortable points
type point struct {
	x int
	y int
}

type points []point

func (p points) Len() int {
	return len(p)
}

func (p points) Less(i, j int) bool {
	return p[i].x < p[j].x
}

func (p points) Swap(i, j int) {
	p[i], p[j] = p[j], p[i]
}