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 
class routers:
    def __init__(self, rs, n):
        self.routers = rs
        self.n = n
    def path(self, router):
        res = [0]*self.n #speed vs memory
        i = 0
        while router != 1:
            res[i] = router
            i += 1
            router = self.routers[router-2]
        res[i] = 1
        return res[i::-1]
if __name__ == "__main__":
    n = int(raw_input())
    rs = map(int, raw_input().split())
    path = routers(rs, n).path(n)
    print ' '.join(map(str, path))
