Language: C++

#include <bits/stdc++.h>
#define REP(i, n)     for(int i = 0;i < n;i++)
#define REPR(i, n)    for(int i = n;i >= 0;i--)
#define FOR(i, m, n)  for(int i = m;i < n;i++)
#define FORR(i, m, n) for(int i = m;i >= n;i--)
#define SORT(v, n) sort(v, v+n);
#define VSORT(v) sort(v.begin(), v.end());
#define VRSORT(v) sort(v.begin(), v.end(),greater<long long>());
#define ALL(X) (X).begin(),(X).end()
#define INF 99999999
#define M_PI 3.14159265358979323846
#define MOD 1000000007

#ifdef __LOCAL
    #define DBG(X) cout << #X << " = " << (X) << endl;
    #define SAY(X) cout << (X) << endl;
#else
    #define DBG(X)
    #define SAY(X)
#endif

#ifdef __LOCAL
    #include <filesystem>
    namespace fs = std::filesystem;
#endif

using namespace std;

using ll = long long int;
using ull = unsigned long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

int dx[]={1, 0, -1, 0, 0};
int dy[]={0, 1, 0, -1, 0};
const int INT_INF = (int)(2e9);
const ll  LL_INF = (ll)(2e18);
const int NIL = -1;
static mt19937 _g(time(nullptr));
 
std::string pad(int num){ char buffer[4]; std::snprintf(buffer, sizeof(buffer), "%03d", num); return buffer;}
inline ll randint(ll a, ll b) { ll w = (_g() << 31LL) ^ _g(); return a + w % (b - a + 1); }
inline void fast_io() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); };
template<typename T> inline T sign(T x) { return T(x > 0) - T(x < 0); }
template<typename T, typename S> inline ostream& operator<<(ostream& os, const pair<T, S> p) { cout << "[" << p.first << ";" << p.second << "]"; return os; }
template<typename T, typename S> inline ostream& operator<<(ostream& os, const map<T, S> p) { for (auto el : p) os << "[" << el.first << " " << el.second << "]"; return os; }
template<typename T> inline ostream& operator<<(ostream& os, const vector<T>& v) { for (auto el : v) os << el << " "; return os; }
template<typename T> inline T fetch() { T ret; cin >> ret; return ret; }
template<typename T> inline vector<T> fetch_vec(int sz) { vector<T> ret(sz); for (auto& elem : ret) cin >> elem; return ret; }

int H,W;
vector<string> A;

// 難しいから一旦飛ばす。

void input(){
    fast_io();
    #ifdef __LOCAL
        fs::path p = __FILE__;
        fs::path input,output;
        input = output = p.parent_path();
        input += string("/input/") + string(p.stem()) + string(".txt");
        output += string("/output/") + string(p.stem()) + string(".txt");
        freopen(input.c_str(), "r", stdin);
        freopen(output.c_str(), "w", stdout);
    #endif
    cin >> H >> W;
    REP(i,H){
        string a;
        cin >> a;
        A.push_back(a);
    }

}

void solve(){
    input();
    ull a=0;
    set<ull> state;
    REP(i,H) REP(j,W){
        if(A[i][j]=='#')
            a |= (1LL<<(i+j*W));
    }
    state.insert(a);
    REP(i,H) REP(j,W){
        set<ull> tmp;
        for(auto s:state){
            // ある行に対する操作
            int t1 = s;
            REP(k,W) t1 |= (1LL<<(i*W+k+1));
            tmp.insert(t1);

            // ある列に対する操作
            ull t2 = s;
            REP(k,H) t2 |= (1LL<<(k*W+j));
            tmp.insert(t2);

            // ある行に対する操作
            ull t3 = s;
            REP(k,W) t3 &= ~(1LL<<(i*W+k+1));
            tmp.insert(t3);
            
            // ある列に対する操作
            ull t4 = s;
            REP(k,H) t4 &= ~(1LL<<(k*W+j));
            tmp.insert(t4);

        }
        set<ull> tmp_set;
        set_union(state.begin(),state.end(),tmp.begin(),tmp.end(),tmp_set.begin());
        state.swap(tmp_set);
    }

    DBG(bitset<60>(a))
    // cout << state << endl;
    cout << state.size() << endl;

}


int main()
{
    solve();
    return 0;
}


Compiler output:
In file included from /usr/include/c++/14/algorithm:61,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:51,
                 from a.cc:1:
/usr/include/c++/14/bits/stl_algo.h: In instantiation of '_OutputIterator std::__set_union(_InputIterator1, _InputIterator1, _InputIterator2, _InputIterator2, _OutputIterator, _Compare) [with _InputIterator1 = _Rb_tree_const_iterator<long long unsigned int>; _InputIterator2 = _Rb_tree_const_iterator<long long unsigned int>; _OutputIterator = _Rb_tree_const_iterator<long long unsigned int>; _Compare = __gnu_cxx::__ops::_Iter_less_iter]':
/usr/include/c++/14/bits/stl_algo.h:5112:41:   required from '_OIter std::set_union(_IIter1, _IIter1, _IIter2, _IIter2, _OIter) [with _IIter1 = _Rb_tree_const_iterator<long long unsigned int>; _IIter2 = _Rb_tree_const_iterator<long long unsigned int>; _OIter = _Rb_tree_const_iterator<long long unsigned int>]'
 5112 |       return _GLIBCXX_STD_A::__set_union(__first1, __last1,
      |                                         ^
a.cc:111:18:   required from here
  111 |         set_union(state.begin(),state.end(),tmp.begin(),tmp.end(),tmp_set.begin());
      |         ~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:5047:25: error: assignment of read-only location '__result.std::_Rb_tree_const_iterator<long long unsigned int>::operator*()'
 5047 |               *__result = *__first1;
      |               ~~~~~~~~~~^~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:5052:25: error: assignment of read-only location '__result.std::_Rb_tree_const_iterator<long long unsigned int>::operator*()'
 5052 |               *__result = *__first2;
      |               ~~~~~~~~~~^~~~~~~~~~~
/usr/include/c++/14/bits/stl_algo.h:5057:25: error: assignment of read-only location '__result.std::_Rb_tree_const_iterator<long long unsigned int>::operator*()'
 5057 |               *__result = *__first1;
      |               ~~~~~~~~~~^~~~~~~~~~~