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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class ProblemA {
	static Scanner in = new Scanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);
	static ArrayList<Integer> adjList[];
	static boolean ans;

	static int dfs(int u) {
		if (adjList[u].size() == 0)
			return 1;
		if (adjList[u].size() < 3) {
			ans = false;
			return 0;
		}
		int leafs = 0;
		for (Integer v : adjList[u]) {
			leafs += dfs(v);
		}
		if (leafs < 3)
			ans = false;
		return 0;
	}

	public static void main(String[] args) throws IOException {
		int n = in.nextInt();
		adjList = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			adjList[i] = new ArrayList<>();
		}
		for (int i = 0; i < n - 1; i++) {
			int x = in.nextInt();
			adjList[x-1].add(i + 1);
		}
		ans = true;
		dfs(0);
		if (ans) {
			out.println("Yes");
		} else
			out.println("No");
		out.flush();
	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner(InputStream s) {
			// TODO Auto-generated constructor stub
			br = new BufferedReader(new InputStreamReader(s));
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public String next() throws IOException {
			if (st == null || !st.hasMoreElements())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}
	}

}