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:
n = int(input())
l = list()
for i in range(n+1):
    l.append([])
# print(n, l)
for i in range(n-1):
    curr = int(input())
    l[curr].append(i+2)
# print(l)

def is_leaf(l, vertex):
    if l[vertex] == []:
        return True
    else:
        return False
f = True
for i in range(1, n+1):
    current_vertex = l[i]
    curr_count = 0
    for child in current_vertex:
        # print('Current parent is {} current child is {}'.format(current_vertex, child))
        if is_leaf(l, child) is True:
            curr_count += 1
    # print(curr_count)
    if curr_count < 3 and (is_leaf(l, i) is False):
        f = False
        break
if f is True:
    print('Yes')
else:
    print('No')