human
Give me a Python code to print "Yes" if the tree is a spruce and "No" otherwise given the following:
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:


The second example:


It is not a spruce, because the non-leaf vertex 1 has only 2 leaf children.

The third example:

class
assistant
#Here is Python code to print "Yes" if the tree is a spruce and "No" otherwise.
 Node:
    def __init__(self,value):
        self.data = value
        self.children = []
    def add_children(self,value):
        self.children.append(Node(value))

class Tree:
    def __init__(self):
        self.root = Node(1)

    def Search(self,value,node = None):
        if node is None:
            node = self.root
        q = None
        if node.data == value:
            return node
        else:
            for i in range(len(node.children)):
                q = self.Search(value,node.children[i])
                if q is not None:
                    return q
        return q

    def Insert(self,value,parent):
        node = self.Search(parent)
        node.add_children(value)

    def is_spruce(self,node = None):
        if node == None:
            node = self.root
        for i in range(len(node.children)):
            spruce = self.is_spruce(node.children[i])
            if not spruce:
                return spruce
        if len(node.children) > 0:
            num = 0
            for i in range(len(node.children)):
                child = node.children[i]
                if len(child.children) == 0:
                    num = num + 1
            if num < 3:
                return False
        return True
if __name__ == "__main__":
    n = int(input())
    tree = Tree()
    for i in range(n-1):
        parent = int(input())
        value = i+2
        tree.Insert(value,parent)
    if tree.is_spruce():
        print("Yes")
    else:
        print("No")