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 
# -*- coding: utf-8 -*-
"""
Created on Sat Oct 13 06:12:10 2018

@author: rafael
"""

class Node(object):
    
    def __init__(self, data,children = [], father = None):
        self.data = data
        self.children = children
        self.father = father

    def add_child(self, obj):
        self.children.append(obj)
    
    def __str__(self):
        exp = str(self.data) + ' '+ str(self.father) + '\n'
        for i in self.children: exp += '\n'+ str(i.data)
        return exp
        
class Tree(dict):
    
    def __add_element__(self,item):
        self.tree.append(item)
        
        
n = int(input())
attach = [int(i) for i in input().split()]
tree = Tree()
tree.__setitem__(1,Node(1))
for i in range(len(attach)):
    tree.__setitem__(i+2,Node(i+2,[],attach[i]))
    tree.__getitem__(attach[i]).add_child(Node(i+2))
    

father = tree.__getitem__(n).father
path = [father]
while father != 1 and father is not None:
    father = tree.__getitem__(father).father
    path.append(father)
    
exp = ''
for i in range(len(path)-1,-1,-1):
    exp +=  str(path[i]) + ' '
exp += str(n)

print(exp)