Language: C++

#include<iostream>
#include<string>
#include<algorithm>

using namespace std;

typedef long long ll;

string a[12];
int pairs[12];
int h, w;

bool check_columns();
bool make_even();
bool make_pair_of_lines(int);

bool check_columns(){
    string b[12];
    for(int i=0;i<h;i++){
        if(b[pairs[i]] == ""){
            b[pairs[i]] = a[i];
        }else{
            b[h-1-pairs[i]] = a[i];
        }
    }

    bool center = (w % 2 == 0);
    bool used[w];
    fill(used, used+w, false);

    for(int j=0;j<w;j++){
        if(used[j]) continue;
        used[j] = true;
        bool same = false;

        for(int jj=0;jj<w;jj++){
            if(used[jj]) continue;

            same = true;
            for(int i=0;i<h;i++){
                if(b[i][j] != b[h-1-i][jj]){
                    same = false;
                    break;
                }
            }
            if(same){
                used[jj] = true;
                break;
            }
        }

        if(!same){
            if(center) return false;
            else center = true;
        }
    }

    return true;
}

bool make_even(){
    h++;
    for(int i=0;i<h-1;i++){
        a[h-1] = a[i];
        pairs[h-1] = -1;
        count();
        if(make_pair_of_lines(0)) return true;
    }
    return false;
}

bool make_pair_of_lines(int paired_line){
    if(h % 2) return make_even();

    if(paired_line == h) return check_columns();

    int pair_line_first = -1;
    for(int i=0;i<h;i++){
        if(pairs[i] == -1){
            if(pair_line_first == -1){
                pair_line_first = i;
                pairs[pair_line_first] = paired_line/2;
                break;
            }
        }
    }

    for(int ii=0;ii<h;ii++){
        if(pairs[ii] == -1){
            pairs[ii] = paired_line/2;
            if(make_pair_of_lines(paired_line+2)) return true;
            pairs[ii] = -1;
        }
    }

    pairs[pair_line_first] = -1;

    return false;
}

int main(){
    cin >> h >> w;
    for(int i=0;i<h;i++) cin >> a[i];

    fill(pairs, pairs+h, -1);
    cout << (make_pair_of_lines(0)?"YES":"NO") << endl;
    return 0;
}

Compiler output:
a.cc: In function 'bool make_even()':
a.cc:66:14: error: no matching function for call to 'count()'
   66 |         count();
      |         ~~~~~^~
In file included from /usr/include/c++/14/algorithm:61,
                 from a.cc:3:
/usr/include/c++/14/bits/stl_algo.h:4025:5: note: candidate: 'template<class _IIter, class _Tp> typename std::iterator_traits< <template-parameter-1-1> >::difference_type std::count(_IIter, _IIter, const _Tp&)'
 4025 |     count(_InputIterator __first, _InputIterator __last, const _Tp& __value)
      |     ^~~~~
/usr/include/c++/14/bits/stl_algo.h:4025:5: note:   candidate expects 3 arguments, 0 provided
In file included from /usr/include/c++/14/algorithm:86:
/usr/include/c++/14/pstl/glue_algorithm_defs.h:101:1: note: candidate: 'template<class _ExecutionPolicy, class _ForwardIterator, class _Tp> __pstl::__internal::__enable_if_execution_policy<_ExecutionPolicy, typename std::iterator_traits<_II>::difference_type> std::count(_ExecutionPolicy&&, _ForwardIterator, _ForwardIterator, const _Tp&)'
  101 | count(_ExecutionPolicy&& __exec, _ForwardIterator __first, _ForwardIterator __last, const _Tp& __value);
      | ^~~~~
/usr/include/c++/14/pstl/glue_algorithm_defs.h:101:1: note:   candidate expects 4 arguments, 0 provided