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 JAVA):

Solution:
    import java.io.*;
     
    public class B913ChristmasSpruce {
     
        public static void main(String[] args) throws IOException {
     
            BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
            BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
     
            int n = Integer.parseInt(in.readLine());
            int[] p = new int[n];
            int[] degree = new int[n];
     
            for (int i = 1; i < n; i++) {
                p[i] = Integer.parseInt(in.readLine());
                p[i]--;
                degree[p[i]]++;
            }
     
            int[] leaf = new int[n];
     
            for (int i = 0; i < n; i++) {
                if (degree[i] == 0) leaf[p[i]]++;
            }
     
            for (int i = 0; i < n; i++) {
                if (degree[i] > 0 && leaf[i] < 3) {
                    out.write("NO");
                    out.flush();
                    return;
                }
            }
     
            out.write("YES");
            out.flush();
        }
     
     
    }