Kernel Knights

Jousting is a medieval contest in which two people ride horses at high speed and try to strike each other with wooden lances. A total of $2n$ knights entered a tournament, $n$ from each of two rival houses. On arrival, every knight challenged exactly one knight of the other house to a duel.

A subset $S$ of the knights is called a kernel when both of these hold.

• No knight in $S$ was challenged by another knight in $S$.
• Every knight outside $S$ was challenged by some knight in $S$.

Given all of the challenges, find a kernel. A kernel always exists.

The first line contains the number of knights in each house, $n$ ($1 \le n \le 100\,000$). The knights of the first house are numbered $1$ through $n$, and the knights of the second house are numbered $n+1$ through $2n$.

The second line contains integers $f_1, f_2, \dots, f_n$, where $f_k$ is the index of the knight challenged by knight $k$ ($n+1 \le f_k \le 2n$).

The third line contains integers $s_1, s_2, \dots, s_n$, where $s_k$ is the index of the knight challenged by knight $n+k$ ($1 \le s_k \le n$).

Print the indices of the knights in the kernel in increasing order on a single line, separated by single spaces.

If several kernels exist, print the lexicographically smallest one. That is, write each kernel as its increasing sequence of indices and print the sequence that comes first lexicographically.