Language: C++

void getPairings(int n,int start=0){
    if(curPairs.size()==n/2) allPairs.push_back(curPairs);
    else{
        for(int i=start; i<n; i++){
            if(chosen[i]) continue;
            chosen[i]=true;
            for(int j=i+1; j<n; j++){
                if(chosen[j]) continue;
                //chosen[i]=true;
                chosen[j]=true;
                curPairs.push_back({i,j});
                getPairings(n, i);
                //chosen[i]=false;
                chosen[j]=false;
                curPairs.pop_back();
            }
            chosen[i]=false;
            //ydone[i]=true;
        }
        
    }
    
}
 
int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int n,m;
    cin>>n>>m;
    
    vector<string> vs(n);
    for(auto&s:vs)cin>>s;
    
    vector<int> cts(26);
    for(auto v:vs){
        for(char c:v){
            cts[c-'a']++;
        }
    }
    int oct=0;
    for(int i=0; i<26; i++){
        oct+=cts[i]%2;
    }
    if(oct>1 || (n%2 && m%2 && !oct) || (oct && !min(n%2,m%2))){
        cout<<"NO";
        return 0;
    }
    if(n==1 || m==1){
        cout<<"YES";
        return 0;
    }
    //cout<<"YES";
    
    getPairings(n);
    
    vector<string> vt(n), vt2(m,string(n,'a'));
    
    for (auto& v:allPairs){
        int sz=v.size();
        for(int i=0; i<sz; i++){
            vt[i]=vs[v[i].first];
            vt[n-1-i]=vs[v[i].second];
        }
        if(n%2){
            vector<bool> used(n);
            for(auto p:v){
                used[p.first]=1;
                used[p.second]=1;
                
            }
            for(int i=0; i<n; i++){
                if(!used[i]){
                    vt[n/2+1]=vs[i];
                }
            }
        }
        for(int i=0; i<n; i++){
            //cout<<vt[i]<<endl;
            for(int j=0; j<m; j++){
                vt2[j][i]=vt[i][j];
            }
        }
        vector<bool> used(m);
        
        bool works=true, invUsed=false;
        for(int i=0; i<m && works; i++){
            if(used[i]) continue;
            auto s=vt2[i];
            //cout<<vt2[i]<<endl;
            reverse(s.begin(),s.end());
            bool found=false;
            for(int j=i+1; j<m && !found; j++){
                if(vt2[j]==s && !used[j]){
                    found=true;
                    used[i]=1;
                    used[j]=1;
                }
            }
            if(!found){
                //cout<<vt2[i]<<endl;
                if(m%2 && vt2[i]==s && !invUsed){
                    used[i]=true;
                    invUsed=true;
                }
                else{
                    works=false;
                }
            }
        }
        if(works){
            cout<<"YES";
            return 0;
        }
        
        
    }
    cout<<"NO";
    
    
    /*
    cout<<allPairs.size()<<endl;
    
    
    for(auto v: allPairs){
        for(auto p:v){
            cout<<"("<<p.first<<","<<p.second<<")";
        }
        cout<<endl;
    }
    */
    
   
    
    return 0;
}

Compiler output:
a.cc: In function 'void getPairings(int, int)':
a.cc:2:8: error: 'curPairs' was not declared in this scope
    2 |     if(curPairs.size()==n/2) allPairs.push_back(curPairs);
      |        ^~~~~~~~
a.cc:2:30: error: 'allPairs' was not declared in this scope
    2 |     if(curPairs.size()==n/2) allPairs.push_back(curPairs);
      |                              ^~~~~~~~
a.cc:5:16: error: 'chosen' was not declared in this scope
    5 |             if(chosen[i]) continue;
      |                ^~~~~~
a.cc:6:13: error: 'chosen' was not declared in this scope
    6 |             chosen[i]=true;
      |             ^~~~~~
a.cc: In function 'int main()':
a.cc:26:5: error: 'ios_base' has not been declared
   26 |     ios_base::sync_with_stdio(0);
      |     ^~~~~~~~
a.cc:27:5: error: 'cin' was not declared in this scope
   27 |     cin.tie(0);
      |     ^~~
a.cc:31:5: error: 'vector' was not declared in this scope
   31 |     vector<string> vs(n);
      |     ^~~~~~
a.cc:31:12: error: 'string' was not declared in this scope
   31 |     vector<string> vs(n);
      |            ^~~~~~
a.cc:31:20: error: 'vs' was not declared in this scope
   31 |     vector<string> vs(n);
      |                    ^~
a.cc:34:12: error: expected primary-expression before 'int'
   34 |     vector<int> cts(26);
      |            ^~~
a.cc:37:13: error: 'cts' was not declared in this scope
   37 |             cts[c-'a']++;
      |             ^~~
a.cc:42:14: error: 'cts' was not declared in this scope
   42 |         oct+=cts[i]%2;
      |              ^~~
a.cc:44:50: error: 'min' was not declared in this scope; did you mean 'main'?
   44 |     if(oct>1 || (n%2 && m%2 && !oct) || (oct && !min(n%2,m%2))){
      |                                                  ^~~
      |                                                  main
a.cc:45:9: error: 'cout' was not declared in this scope
   45 |         cout<<"NO";
      |         ^~~~
a.cc:49:9: error: 'cout' was not declared in this scope
   49 |         cout<<"YES";
      |         ^~~~
a.cc:56:20: error: 'vt' was not declared in this scope
   56 |     vector<string> vt(n), vt2(m,string(n,'a'));
      |                    ^~
a.cc:56:27: error: 'vt2' was not declared in this scope
   56 |     vector<string> vt(n), vt2(m,string(n,'a'));
      |                           ^~~
a.cc:58:18: error: 'allPairs' was not declared in this scope
   58 |     for (auto& v:allPairs){
      |                  ^~~~~~~~
a.cc:65:20: error: expected primary-expression before 'bool'
   65 |             vector<bool> used(n);
      |                    ^~~~
a.cc:67:17: error: 'used' was not declared in this scope
   67 |                 used[p.first]=1;
      |                 ^~~~
a.cc:72:21: error: 'used' was not declared in this scope
   72 |                 if(!used[i]){
      |                     ^~~~
a.cc:83:16: error: expected primary-expression before 'bool'
   83 |         vector<bool> used(m);
      |                ^~~~
a.cc:87:16: error: 'used' was not declared in this scope
   87 |             if(used[i]) continue;
      |                ^~~~
a.cc:90:13: error: 'reverse' was not declared in this scope
   90 |             reverse(s.begin(),s.end());
      |             ^~~~~~~
a.cc:93:34: error: 'used' was not declared in this scope
   93 |                 if(vt2[j]==s && !used[j]){
      |                                  ^~~~
a.cc:102:21: error: 'used' was not declared in this scope
  102 |                     used[i]=true;
      |                     ^~~~
a.cc:111:13: error: 'cout' was not declared in this scope
  111 |             cout<<"YES";
      |             ^~~~
a.cc:117:5: error: 'cout' was not declared in this scope
  117 |     cout<<"NO";
      |     ^~~~