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:
#H18_B

n = int(input())

ls = []

for i in range(0, n - 1):
    ls.append([i + 2, int(input())])

def findValid(ls, o):
    found = True
    l = 0
    lfs = 0
    for i in ls:
        if i[1] == o:
            lfs += 1
            fv = findValid(ls, i[0])
            if fv[1] == 0:
                l += 1
            if (fv[1] < 3 and fv[1] > 0) or not fv[0]:
                found = False
    if (l != 0 or lfs != 0) and l < 3:
        found = False
    return [found, l]

wds = ["No", "Yes"]

fv = findValid(ls, 1)
print(wds[fv[0]])