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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <iomanip>
#include <string>
#include <vector>
#include <map>
#include <algorithm>  // std::unique
#include <cmath>
#include <limits.h>
#include <queue>
#include <unordered_map>
#include <sstream>      // std::ostringstream
#include <bitset>
#include <iomanip>
#include <functional>
#include <set>


#define _USE_MATH_DEFINES
#include <math.h>
using namespace std;

using ll = long long;
constexpr auto PrimeBigNum10_9_7 = 1000000007;
const long long INF = 1LL << 60;

#define OUTPUT_DEBUG_LOG

template <typename T>
void DisplayAnswer(const T& v) {
	cout << v << endl;
}
template <typename T>
void DisplayAnswers(const vector<T>& vs) {
	for (const auto& v : vs) {
		cout << v << endl;
	}
}

template <typename T>
void DisplayAnswerOneLine(const vector<T>& vs) {
	for (const auto& v : vs) {
		cout << v << ' ';
	}
	cout << endl;
}


std::vector<std::string> split(const std::string &str, char sep)
{
	std::vector<std::string> v;
	std::stringstream ss(str);
	std::string buffer;
	while (std::getline(ss, buffer, sep)) {
		v.push_back(buffer);
	}
	return v;
}



template<class T>
void chmin(T& a, T b) {
	if (a > b) {
		a = b;
	}
}


// 素数判定
template <typename T>
bool IsPrimeNumber(T value) {

	for (int i = 2; i * i <= value; ++i) {
		if ((value % i) == 0) {
			return true;
		}
	}
	return false;
}

// 桁数判定
template <typename T>
T GetFigureLength(T value) {
	T figure = 1;
	while (value >= 10) {
		value /= 10;
		++figure;
	}
	return figure;
}

// 素因数分解結果
template <typename T>
map<T, T> GetPrimeFactorize(T value) {

	map<T, T> res;

	for (T i = 2; i * i <= value; ++i) {
		if ((value%i) != 0)	continue;

		T count = 0;
		while ((value % i) == 0) {
			value /= i;
			++count;
		}

		res[i] = count;
	}

	if (value != 1) {
		res[value] = 1;
	}
	return res;
}


void DebugPrint(const vector<ll>& vec) {
	cout << "{";
	for (auto itr = vec.begin(); itr != vec.end(); ++itr) {
		cout << *itr << ",";
	}
	cout << "}" << endl;
}

// valueが2のx乗以下である計算
ll calc2x(ll value) {
	ll n = 0;
	while (value > 0) {
		value /= 2;
		++n;
	}
	return n;
}



struct Vec2 {
	double x;
	double y;

	void rotate(double rad) {
		double s = sin(rad);
		double c = cos(rad);
		double tmpX = this->x*c - this->y*s;
		double tmpY = this->x*s + this->y*c;
		this->x = tmpX;
		this->y = tmpY;
	}
};

void FuncA() {
	ll m;
	cin >> m;

	while (m > 0) {
		m -= 1000;
	}
	DisplayAnswer(-m);
}

void FuncB() {
	unordered_map<string, int> map;

	map["AC"]=0;
	map["WA"] = 0;
	map["TLE"] = 0;
	map["RE"] = 0;

	ll n;
	cin >> n;
	while (n--) {
		string str;
		cin >> str;
		map[str]++;
	}

	cout << "AC x " << map["AC"] << endl;
	cout << "WA x " << map["WA"] << endl;
	cout << "TLE x " << map["TLE"] << endl;
	cout << "RE x " << map["RE"] << endl;
}
namespace C {
	ll map[6][6] = {};
	int calcSum(bitset<6> bh, bitset<6>bw) {
		ll sum = 0;
		for (ll i = 0; i < 6; ++i) {
			if (bh[i] == 0)	continue;
			for (ll j = 0; j < 6; ++j) {
				if (bw[j]) {
					sum += map[i][j];
				}
			}
		}
		return sum;

	}

	int CalcFuncC() {
		ll H, W, K;
		cin >> H >> W >> K;
		ll mapHs[6] = {};

		ll black = 0;
		for (ll i = 0; i < H; ++i) {
			for (ll j = 0; j < W; ++j) {
				char c;
				cin >> c;
				map[i][j] = (c == '#') ? 1 : 0;
				black += map[i][j];
				mapHs[i] += map[i][j];
			}
		}
		ll hMax = 1 << H;
		ll wMax = 1 <<W;

		ll answer = 0;
		for (ll i = 0; i < hMax; ++i) {
			bitset<6> bh = i;
			ll n = 0;
			for (ll k = 0; k < 6; ++k) {
				if (bh[k]) {
					n += mapHs[k];
				}
			}
			if (n < K)	continue;

			for (ll j = 0; j < wMax; ++j) {
				ll sum = calcSum(bh, j);
				if (sum == K) {
					bitset<6> bw = j;
					answer++;
				}
			}
		}

		return answer;

	}
}

void FuncC() {
	DisplayAnswer(C::CalcFuncC());
}
int main(void) {

	FuncC();

	return 0;
}