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A. Bmail Computer Network

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOnce 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.

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.

Examples

Input

8

1 1 2 2 3 2 5

Output

1 2 5 8

Input

6

1 2 3 4 5

Output

1 2 3 4 5 6

Input

7

1 1 2 3 4 3

Output

1 3 7

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