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 
from collections import defaultdict as defdic
from collections import deque

class Graph:
    def __init__(self):
        self.graph = defdic(list)
    def addedge(self,u,v):
        self.graph[u].append(v)
    def BFS(self,u):
        visited = defdic(int)
        qu=deque()
        qu.append(u)
        visited[u]=True
        x=[]
        while qu:
            s=qu.popleft()
            x.append(s)
            for i in self.graph[s]:
                if visited[i]==0:
                    qu.append(i)
                    visited[i]=True
        #print(x)
    def DFSUtil(self, s, visited,k): 
        stack = []  
        dpt={} 
        stack.append(s)
        while (len(stack) != 0):
            s = stack[-1]
            if (not visited[s]): 
                k.add(s)
                visited[s] = True
                dpt[s]=len(k)
            else :
                s=stack.pop()
                k.remove(s)
                continue
            if s==self.lens:
                k=sorted(k)
                for j in k:
                    print(j,end=" ")
                return 0
            l=0  
            for i in self.graph[s]:
                if not visited[i]:
                    stack.append(i)
                    l+=1
        return 1
      
    def DFS(self): 
        
        k=set()
        visited = defdic(int)
        for i in self.graph: 
            if (not visited[i]): 
                x=self.DFSUtil(i, visited,k)
                if x==0:
                    return
        #print(k)
n=int(input())
s=list(map(int,input().split()))
g=Graph()
for i in range(2,n):
    g.addedge(s[i-2],i)
g.addedge(s[n-2],n)
g.lens=n
k=g.DFS()
