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:
node_num = int(input())

class Tree:
    def __init__(self, cargo, *children):
        self.cargo = cargo
        self.children = list(children)
        self.addNode = lambda node: self.children.append(node)

    def __str__(self):
        return str(self.cargo)


def bfs(tree, target):
    q = [tree]
    while q:
        if q[0].cargo == target:
            return q[0]
        if q[0].children:
            for y in q[0].children:
                q.append(y)
        del q[0]
    return False


candidate = Tree(1)
for x in range(node_num - 1):
    parent_index = int(input())
    location = bfs(candidate, parent_index)
    if location:
        location.addNode(Tree(x + 2))


check_q = [candidate]

while check_q:
    leaf = 0
    for x in check_q[0].children:
        if x.children:
            check_q.append(x)
        else:
            leaf += 1
    if leaf < 3:
        print('No')
        exit()
    else:
        del check_q[0]


print('Yes')