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:
import sys

input = sys.stdin.readline


############ ---- Input Functions ---- ############
def inp():
    return (int(input()))


def inlt():
    return (list(map(int, input().split())))


def insr():
    s = input()
    return (list(s[:len(s) - 1]))


def invr():
    return (map(int, input().split()))

def explore(adj,i):
    count=[]
    q=[i]
    while(q!=[]):
        i=min(q)
        q.remove(i)
        if visited[i]!=1:
            visited[i]=1
            count+=[i+1]
            q+=adj[i]
    return count

x=0
n=inp()
adj=[[] for i in range(n)]
for i in range(n-1):
    u=inp()
    if u !=-1 and u-1!= i+1:
        adj[u-1].append(i+1)

for i in range(n):
    if adj[i]==[]:
        continue
    else:
        a=0
        for j in adj[i]:
            if adj[j]==[]:
                a+=1
        if a<3:
            x=1
            break

if x==1:
    print("NO")
else:
    print("YES")