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:
class TreNode:
    def __init__(self,parent):
        self.children = []
        self.parent = parent
    def isLeaf(self):
        return self.children == []
 
AllNodes = {}
 
AllNodes[1] = TreNode(-1)
 
a = int(input())
 
if a < 2:
    print('No')
    quit()
 
for i in range(2,a+1):
    ThisParent = int(input())
    if i in list(AllNodes.keys()):
        AllNodes[i].parent = ThisParent
    else:
        AllNodes[i] = TreNode(ThisParent)
    if ThisParent not in list(AllNodes.keys()):
        AllNodes[ThisParent] = TreNode(-1)
    AllNodes[ThisParent].children.append(i)
 
for node in list(AllNodes.keys()):
    #print(node,AllNodes[node].children)
    thisnodeleafcount = 0
    for child in AllNodes[node].children:
        if len(AllNodes[child].children) == 0:
            thisnodeleafcount += 1
    if thisnodeleafcount < 3 and not AllNodes[node].isLeaf():
        print('No')
        quit()
 
print('Yes')