GPT答：

7i24.cn

```cpp
#include <iostream>
#include <unordered_set>
using namespace std;

const int MAXN = 105;
char matrix[MAXN][MAXN];
int n;
unordered_set<string> palindromeSet;

void dfs(int x, int y, string path) {
    if (x == n && y == n) {
        string reversePath = path;
        reverse(reversePath.begin(), reversePath.end());
        palindromeSet.insert(path + reversePath);
        return;
    }
    
    if (x + 1 <= n) {
        dfs(x+1, y, path + matrix[x+1][y]);
    }
    
    if (y + 1 <= n) {
        dfs(x, y+1, path + matrix[x][y+1]);
    }
}

int main() {
    cin >> n;
    
    for (int i = 0; i < MAXN; i++) {
        for (int j = 0; j < MAXN; j++) {
            matrix[i][j] = ' ';
        }
    }
    
    for (int i = 1; i <= n; i++) {
         for(int j=1;j<=n;j++){
             cin>>matrix[i][j];
         }   
     }

     dfs(0,0,string(1,matrix[0][0]));
     
     cout<<palindromeSet.size()<<endl;

     return 0;
}
```