Kernel Knights

문제

Jousting is a medieval contest that involves people on horseback trying to strike each other with wooden lances while riding at high speed. A total of 2n knights have entered a jousting tournament – n knights from each of the two great rival houses. Upon arrival, each knight has challenged a single knight from the other house to a duel.

A kernel is defined as some subset S of knights with the following two properties:

• No knight in S was challenged by another knight in S.
• Every knight not in S was challenged by some knight in S.

Given the set of the challenges issued, find one kernel. It is guaranteed that a kernel always exists.

입력

The first line contains an integer n (1 ≤ n ≤ 100 000) – the number of knights of each house. The knights from the first house are denoted with integers 1 through n, knights from the second house with integers n + 1 through 2n.

The following line contains integers f₁, f₂, . . . , f_n – the k-th integer f_k is the index of the knight challenged by knight k (n + 1 ≤ f_k ≤ 2n).

The following line contains integers s₁,s₂, . . . ,s_n – the k-th integer s_k is the index of the knight challenged by knight n + k (1 ≤ s_k ≤ n).

출력

Output the indices of the knights in the kernel on a single line. If there is more than one solution, you may output any one.

4
5 6 7 7
1 3 2 3

1 2 4 8