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 CodeforcesTask1057ASolution:
    def __init__(self):
        self.result = ''
        self.n = 0
        self.routers = []

    def read_input(self):
        self.n = int(input())
        self.routers = [int(x) for x in input().split(" ")]

    def process_task(self):
        s = [self.n]
        x = self.n
        while x != 1:
            step = self.routers[x - 2]
            x = step
            s.append(step)
        while s:
            print(s.pop(-1), end=" ")

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask1057ASolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())
