Language: C++

using namespace std;
 
int h, w;
char s[12][13];
string ss[12];
int a[12];
int b[12];
 
void dfs1(int x, bool f) {
    if (x == w) {
        puts("YES");
        exit(0);
    } else if (b[x] != -1) {
        dfs1(x + 1, f);
    } else {
        int i, j;
        
        for (i = x + 1; i < w; i++) {
            if (b[i] != -1) continue;
            
            for (j = 0; j < h; j++) {
                if (s[j][x] != s[a[j]][i]) break;
            }
            
            if (j == h) {
                b[x] = i;
                b[i] = x;
                
                dfs1(x + 1, f);
                
                b[x] = b[i] = -1;
            }
        }
       
        
        if (!f) {
            for (j = 0; j < h; j++) {
                if (s[j][x] != s[a[j]][x]) break;
            }
            
            if (j == h) {
                b[x] = x;
                
                dfs1(x + 1, true);
                
                b[x] = -1;
            }
        }
    }
}
 
void dfs2(int x, bool f) {
    if (x == h) {
        dfs1(0, w % 2 == 0);
    } else if (a[x] != -1) {
        dfs2(x + 1, f);
    } else {
        int i;
        
        for (i = x + 1; i < h; i++) {
            if (a[i] != -1) continue;
            if (ss[x] != ss[i]) continue;
            
            a[x] = i;
            a[i] = x;
            
            dfs2(x + 1, f);
            
            a[x] = a[i] = -1;
        }
        
        if (!f) {
            a[x] = x;
            
            dfs2(x + 1, true);
            
            a[x] = -1;
        }
    }
}
 
int main() {
    int i;
    
    scanf("%d %d", &h, &w);
    
    for (i = 0; i < h; i++) scanf("%s", s[i]);
    
    for (i = 0; i < h; i++) {
        ss[i] = s[i];
        sort(ss[i].begin(), ss[i].end());
    }
    
    for (i = 0; i < h; i++) a[i] = -1;
    for (i = 0; i < w; i++) b[i] = -1;
    
    dfs2(0, h % 2 == 0);
    
    puts("NO");
    
    return 0;
}

Compiler output:
a.cc:5:1: error: 'string' does not name a type
    5 | string ss[12];
      | ^~~~~~
a.cc: In function 'void dfs1(int, bool)':
a.cc:11:9: error: 'puts' was not declared in this scope
   11 |         puts("YES");
      |         ^~~~
a.cc:12:9: error: 'exit' was not declared in this scope
   12 |         exit(0);
      |         ^~~~
a.cc:1:1: note: 'exit' is defined in header '<cstdlib>'; this is probably fixable by adding '#include <cstdlib>'
  +++ |+#include <cstdlib>
    1 | using namespace std;
a.cc: In function 'void dfs2(int, bool)':
a.cc:62:17: error: 'ss' was not declared in this scope; did you mean 's'?
   62 |             if (ss[x] != ss[i]) continue;
      |                 ^~
      |                 s
a.cc: In function 'int main()':
a.cc:85:5: error: 'scanf' was not declared in this scope
   85 |     scanf("%d %d", &h, &w);
      |     ^~~~~
a.cc:90:9: error: 'ss' was not declared in this scope; did you mean 's'?
   90 |         ss[i] = s[i];
      |         ^~
      |         s
a.cc:91:9: error: 'sort' was not declared in this scope; did you mean 'short'?
   91 |         sort(ss[i].begin(), ss[i].end());
      |         ^~~~
      |         short
a.cc:99:5: error: 'puts' was not declared in this scope
   99 |     puts("NO");
      |     ^~~~