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.

Input

The first line contains integer number n (2 ≤ n ≤ 200000) — the number of the routers. The following line contains n-1 integers p_2, p_3, ..., p_n (1 ≤ 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

inputFormat

Input

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

outputFormat

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

样例

8
1 1 2 2 3 2 5

1 2 5 8

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