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 18 13:12:13 2020

@author: lenovo
"""

from collections import defaultdict
from collections import deque

class graph:
    def __init__(self):
        self.g=defaultdict(list)
    def addedge(self,u,v):
        self.g[u].append(v)
def router(values):
    gr=graph()
    for i in range(len(values)):
        gr.addedge(values[i], i+2)
    return gr.g

def isleaf(node,gr):
    if len(gr[node])==0:
        return True
    return False

def christmas(gr,start,visited):
    q=deque()
    q.append(start)
    visited[start]=True
    count=0
    while q:
        count=0
        value=q.popleft()
        for val in gr[value]:
            if not isleaf(val,gr):
                q.append(val)
                visited[val]=True
            else:
                visited[val]=True
                count=count+1
        if count<3:
            return 'No'
    if count<3:
        return 'No'
    return 'Yes'
n=int(input())
values=[]
for i in range(n-1):
    value=int(input())
    values.append(value)
gr=router(values)
visited=[False]*(n+1)
print(christmas(gr, 1, visited))