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:
n=int(input())
dic={}
l_del=[]
for i in range(2,n+1):
    x=int(input())
    dic[i]=x
    if x in dic.keys():
        del dic[x]
        l_del.append(x)
l=list(dic.values())
l_del=list(set(l_del))
for i in l_del:
    if i not in l:
        l.append(i)
l.sort()

judge=0
z=1
for i in l:
    if i==z:
        judge=judge+1
        z=i
    elif i!=z:
        if judge>=3:
            z=i
            judge=1
        else:
            judge=-1
            break
if judge>=3:
    print("YES")
else:
    print("NO")