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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.List;
import java.util.Scanner;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author hsy
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        static boolean flag;
        static TaskB.Vec[] vecs;

        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            vecs = new TaskB.Vec[n + 1];
            for (int i = 0; i < n + 1; i++) {
                vecs[i] = new TaskB.Vec();
            }
            for (int i = 1; i <= n - 1; i++) {
                vecs[in.nextInt()].list.add(i + 1);
            }
            flag = true;
            dfs(1);
            if (flag) out.println("Yes");
            else out.println("No");
        }

        private void dfs(int i) {
            if (!flag || vecs[i].list.isEmpty()) return;
            int count = vecs[i].list.size();
            for (int x : vecs[i].list) {
                if (!vecs[x].list.isEmpty()) {
                    count--;
                }
            }
            if (count < 3) {
                flag = false;
                return;
            } else {
                for (int x : vecs[i].list) {
                    dfs(x);
                }
            }
        }

        static class Vec {
            List<Integer> list = new ArrayList<>();

        }

    }
}