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:
# chtistmas spruce
import sys
import math
import collections
from pprint import pprint as pp
mod = 1000000007
MAX = 10**10


def vector(size, val=0):
    vec = [val for i in range(size)]
    return vec


def matrix(rowNum, colNum, val=0):
    mat = []
    for i in range(rowNum):
        collumn = [val for j in range(colNum)]
        mat.append(collumn)
    return mat


n = int(input())
a = matrix(n + 1, 0)
val = vector(n + 1, -1)


def dfs(x, par):
    if len(a[x]) == 0:
        val[par] += 1
    else:
        for i in a[x]:
            dfs(i, x)


for i in range(2, n + 1):
    x = int(input())
    a[x].append(i)

for i in range(1, n + 1):
    if len(a[i]) != 0:
        val[i] = 0
dfs(1, 0)
for i in range(1, n + 1):
    if val[i] != -1 and val[i] < 3:
        print('No')
        sys.exit()
print("Yes")