Bmail Computer Network
Description
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.
Input
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.
Output
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.
Samples
8
1 1 2 2 3 2 5
1 2 5 8
6
1 2 3 4 5
1 2 3 4 5 6
7
1 1 2 3 4 3
1 3 7