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 

def Solution():
    routers = []
    path = []
    n = int(input())
    lis = input().split()

    # for x in lis:
    #     routers.append(int(x))
    i = n

    while(i != 1):
        path.append(i)
        next_element = int(lis[i-2])
        i = next_element
    path.append(1)

    x = ''
    for i in range(0, len(path)):
        if x != '':
            x = x+' '
        x=x+str(path.pop())
    print(x)


if __name__ == '__main__':
    Solution()