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 pi — the index of the router to which the i-th router was connected after being purchased (pi<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≤n≤200000) — the number of the routers. The following line contains n−1 integers p2,p3,...,pn (1≤pi<i), where pi 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.