Kernel Knights

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.

Input

The first line contains an integer $n(1\le n\le 10^5)$ — 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 $f_1,f_2,...,f_n$ — the $k$-th integer $f_k$ is the index of the knight challenged by knight $k(n+1\le f_k\le 2n)$.

The following line contains integers $s_1,s_2,...,s_n$ — the $k$-th integer $s_k$ is the index of the knight challenged by knight $n+k(1\le s_k\le n)$.

Output

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.

Examples