class Solution {
public:
    void rotate(vector<vector<int> > &matrix) {
        int n = matrix.size();
        if(n == 0) return;
        for(int i = 0; i < (n / 2); ++i) {
            int top = i, bottom = n - 1 - i;
            int left = top, right = bottom;
            for(int j = i; j < n - 1 - i; ++j) {
                int tmp = matrix[top][j];
                matrix[top][j] = matrix[n - 1 - j][left];
                matrix[n - 1 - j][left] = matrix[bottom][n - 1 - j];
                matrix[bottom][n - 1 - j] = matrix[j][right];
                matrix[j][right] = tmp;
            }
        }
    }
};

/*
 * clockwise rotate
 * first reverse up to down, then swap the symmetry 
 * 1 2 3     7 8 9     7 4 1
 * 4 5 6  => 4 5 6  => 8 5 2
 * 7 8 9     1 2 3     9 6 3
*/
void rotate(vector<vector<int> > &matrix) {
    reverse(matrix.begin(), matrix.end());
    for (int i = 0; i < matrix.size(); ++i) {
        for (int j = i + 1; j < matrix[i].size(); ++j)
            swap(matrix[i][j], matrix[j][i]);
    }
}

/*
 * anticlockwise rotate
 * first reverse left to right, then swap the symmetry
 * 1 2 3     3 2 1     3 6 9
 * 4 5 6  => 6 5 4  => 2 5 8
 * 7 8 9     9 8 7     1 4 7
*/
void anti_rotate(vector<vector<int> > &matrix) {
    for (auto vi : matrix) reverse(vi.begin(), vi.end());
    for (int i = 0; i < matrix.size(); ++i) {
        for (int j = i + 1; j < matrix[i].size(); ++j)
            swap(matrix[i][j], matrix[j][i]);
    }
}