Problem: Consider a rooted tree. A rooted tree has one special vertex called the root. All edges are directed from the root. Vertex u is called a child of vertex v and vertex v is called a parent of vertex u if there exists a directed edge from v to u. A vertex is called a leaf if it doesn't have children and has a parent.

Let's call a rooted tree a spruce if its every non-leaf vertex has at least 3 leaf children. You are given a rooted tree, check whether it's a spruce.

The definition of a rooted tree can be found [here](https://goo.gl/1dqvzz).

Input

The first line contains one integer n — the number of vertices in the tree (3 ≤ n ≤ 1 000). Each of the next n - 1 lines contains one integer pi (1 ≤ i ≤ n - 1) — the index of the parent of the i + 1-th vertex (1 ≤ pi ≤ i).

Vertex 1 is the root. It's guaranteed that the root has at least 2 children.

Output

Print "Yes" if the tree is a spruce and "No" otherwise.

Examples

Input

4
1
1
1


Output

Yes


Input

7
1
1
1
2
2
2


Output

No


Input

8
1
1
1
1
3
3
3


Output

Yes

Note

The first example:

<image>

The second example:

<image>

It is not a spruce, because the non-leaf vertex 1 has only 2 leaf children.

The third example:

<image>

Solution (in PYTHON3):

Solution:
# -*- coding: utf-8 -*-
"""
Created on Fri Dec 27 11:35:21 2019

@author: DELL
"""

def isleafnode(e):
    if len(e)==0:
        return 1
    else:
        return 0
a=int(input())
l=[[] for i in range(a)]
for i in range(2,(a+1)):
    k=int(input())
    l[k-1].append(i)
r=[]
for j in range(1,a):
   if len(l[j])!=0:
       r.append(j)
if len(r)==0:
    if len(l[0])>=3:
        print("Yes")
    else:
        print("No")
else:
    k=0
    for i in range(len(r)):
       if len(l[r[i]])<3:
           k+=1
       elif len(l[r[i]])>=3:
           count=0
           for t in range(len(l[r[i]])):
               if isleafnode(l[l[r[i]][t]-1])==1:
                   count+=1
           if count<3:
               k+=1
           else:
               y=0
               for t in range(len(l[0])):
                   if isleafnode(l[l[0][t]-1])==1:
                       y+=1
               if y<3:
                   k+=1
    if k==0:
        print("Yes")
    else:
        print("No")