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())
 
adjList = []
for i in range(0, n):
    adjList.append([])
 
for i in range(0, n-1):
    inputLine = int(input())
 
    adjList[inputLine-1].append(i+1)
    adjList[i+1].append(inputLine-1)
 
#print(adjList)
 
subTrees = []
for i in range(0, n):
    subTrees.append(-1)
 
visited = []
for i in range(0, n):
    visited.append(False)
 
roots = []
for i in range(0, n):
    roots.append(False)

 
def dfs(x):
    #print(subTrees)
    totalSize = 0
    visited[x] = True
    isLeaf = True
    if len(adjList[x]) > 1:
        roots[x] = True
    for i in range(0, len(adjList[x])):
        
        if visited[adjList[x][i]]:
            continue
            
        child = adjList[x][i]
        #print(child)
        dfs(child)
        if roots[child] == True:
            totalSize -= 1
        totalSize += 1
    if roots[x] == False:
        subTrees[x] = -100000
    else:
        subTrees[x] = totalSize
    #print(roots)
 
dfs(0)
#print(subTrees)
isSpruce = True
if n == 3:
    print("No")
else:
    for i in range(0, n):
        if subTrees[i] < 3 and subTrees[i] != -100000:
            print("No")
            isSpruce = False
            break
     
    if isSpruce:
        print("Yes")