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.
The first line contains an integer n (1≤n≤105) — 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,...,fn — the k-th integer fk is the index of the knight challenged by knight k (n+1≤fk≤2n).
The following line contains integers s1,s2,...,sn — the k-th integer sk is the index of the knight challenged by knight n+k (1≤sk≤n).
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.