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