A. Bmail Computer Networktime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard 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.InputThe 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.OutputPrint 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.ExamplesInput81 1 2 2 3 2 5Output1 2 5 8 Input61 2 3 4 5Output1 2 3 4 5 6 Input71 1 2 3 4 3Output1 3 7 
Input81 1 2 2 3 2 5
Output1 2 5 8 
['*special problem', 'dfs and similar', 'trees', '*900']