Since Max is heading off to university, he needs to create a course schedule for ~N~ courses.

However, each course has ~C_i~ prerequisites, and Max cannot schedule properly.

Can you tell Max the order to take his courses to satisfy the prerequisites?

Constraints

~1 \le N \le 2 \times 10^5~

~0 \le C_i < N~

~\sum_{i=1}^N C_i \le \min(\frac{N(N-1)}{2}, 2 \times 10^5)~

It is always possible to generate a course schedule that does not conflict (i.e., it is possible to take every course without missing a prerequisite).

Subtask 1 [40%]

~1 \le N \le 10~

Subtask 2 [60%]

No additional constraints.

Input Specification

The first line will contain an integer, ~N~, the number of courses in the schedule.

The next ~N~ lines will contain an integer, ~C_i~, and ~C_i~ integers, representing the number of prerequisites for the ~i^\text{th}~ course and its prerequisites.

Output Specification

Output any valid permutation of the ~N~ courses, where each course is not missing a prerequisite when it is taken.

Sample Input

5
0
0
3 1 2 5
3 1 2 3
1 2

Sample Output

1 2 5 3 4