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 PYTHON):

Solution:
import sys    
n = int(raw_input())    
    
arr = [[] for i in xrange(1001)]    
for i in xrange(n-1):    
  idx = int(raw_input())    
  arr[idx-1].append(i+1)    
    
def find(idx, arr):                                                             
  if len(arr[idx]) == 0: return 1                                               
  cnt = 0                                                                       
  for child in arr[idx]:                                                        
    cnt += find(child, arr)                                                     
  if cnt < 3:                                                                   
    print "No"                                                                  
    sys.exit()                                                                  
  return 0                                                                      
                                                                                
find(0, arr)                                                                    
print "Yes"