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:
tree = {}

def isLeaf(x):
    # print(tree[x])
    return len(tree[x])==0


def searchTree():
    queue = []
    for i in tree.keys():
        queue.append(i)
    branch = 1
    while(len(queue)>0):
        # print("queue", queue)
        # print("obj", tree[queue[0]])
        if(isLeaf(queue[0])):
            # print("is leaf")
            queue.pop(0)
            continue;
        else:
            # print("is not leaf")
            for j in tree[queue[0]]:
                queue.append(j)
            leafs = len(tree[queue[0]])
            # print("leaf",leafs)
            for j in tree[queue[0]]:
                # print(j,isLeaf(j))
                if(not isLeaf(j)):
                    leafs -=1

            # print("leaf",leafs)
            if(leafs<3 or leafs == -1):
                branch = 0
            queue.pop(0)
    return branch


n = int(input())

# root = theNode(1)



for i in range(1,n+1):
    tree[i] = []
# tree.append({1:[]})

for i in range(2,n+1):

    # y = theNode(i)
    # print(i,y)

    x = int(input())
    tree[x].append(i)
    # print(theNode(x))
    # theNode(x).add_child(y)
    # print(theNode(x).children)

# print(tree)

print("Yes" if searchTree() == 1 else "No")