A12107 | Bmail Computer Network

Once upon a time there was only one router in the well-known company Bmail. Years went by and over time new routers were purchased. Every time they bought a new router, they connected it to one of the routers bought before it. You are given the values $p_i$ — the index of the router to which the $i$ -th router was connected after being purchased ( $p_i < i$ ).

There are $n$ routers in Boogle in total now. Print the sequence of routers on the path from the first to the $n$ -th router.

The first line contains integer number $n$ ( $2 \le n \le 200000$ ) — the number of the routers. The following line contains $n-1$ integers $p_2, p_3, \dots, p_n$ ( $1 \le p_i < i$ ), where $p_i$ is equal to index of the router to which the $i$ -th was connected after purchase.

Print the path from the $1$ -st to the $n$ -th router. It starts with $1$ and ends with $n$ . All the elements in the path should be distinct.