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 math
import atexit
import io
import sys
 
# input = sys.stdin.readline
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER
 
@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
 
def array_to_string(a):
    s = ""
    for i in a:
        s += str(i)
    return s

def gcd(a,b): 
    if a == 0: 
        return b 
    return gcd(b % a, a) 
  
def lcm(a,b): 
    return (a*b) / gcd(a,b) 
 
# t = int(input())
# while t>0:
#     t = t-1
n = int(input())
tree = dict()
for i in range(1,n+1):
    tree[i] = []
for i in range(1,n):
    inp = int(input())
    tree[inp].append(i+1)
k = 0
# print("tree",tree)
for k,v in tree.items():
    # print(k,v)
    if len(v) >= 3:
        c = 0
        for node in v:
            if len(tree[node]) == 0:
                c += 1
        if c >= 3:
            pass
        else:
            k = 1
            break
    elif len(v) == 0:
        pass
    else:
        k = 1
        break
if  k == 1:
    print("No")
else:
    print("Yes")