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:
from collections import defaultdict
G = defaultdict(list)
 
def addEdge(a,b):
    G[a].append(b)
    G[b].append(a)
 
N =int(input())
for i in range(N-1):
    v = int(input())
    addEdge(i+2,v)
leaf = {}
for i,j in G.items():
    if len(j)==1:
        leaf[i] = 1
#print(leaf,G)
f=0
for i,j in G.items():
    if leaf.get(i,-1) == -1:
        count = 0
        for k in j:
            if leaf.get(k,-1) == 1:
                count+=1
        if count<3:
            f=1
            break
if f==0:
    print("Yes")
else:
    print("No")