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.*;
import java.util.*;

public class ChristmasSpruce {

	public static void main(String[] args) throws Exception {
		FastScanner sc = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		run(sc, out);
		out.close();
	}

	public static void run(FastScanner sc, PrintWriter out) throws Exception {
		int N = sc.nextInt();
		ArrayList<Integer>[] arr = new ArrayList[N];
		for (int i = 0; i < N; i++) {
			arr[i] = new ArrayList<>();
		}
		for (int i = 1; i < N; i++) {
			arr[sc.nextInt() - 1].add(i);
		}
		for (int i = 0; i < N; i++) {
			if (arr[i].isEmpty()) continue;
			int count = 0;
			for (int c : arr[i]) {
				if (arr[c].isEmpty()) {
					count++;
				}
			}
			if (count < 3) {
				System.out.println("No");
				return;
			}
		}
		System.out.println("Yes");
	}

	static class FastScanner {
		final private int BUFFER_SIZE = 1 << 20;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public FastScanner(InputStream stream) {
			din = new DataInputStream(stream);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public FastScanner(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		String nextLine() throws IOException {
			int c = read();
			while (c != -1 && isEndline(c))
				c = read();
			if (c == -1) {
				return null;
			}
			StringBuilder res = new StringBuilder();
			do {
				if (c >= 0) {
					res.appendCodePoint(c);
				}
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		String next() throws Exception {
			int c = readOutSpaces();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg) c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg) return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg) c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg) return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg) c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg) return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1) buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead) fillBuffer();
			return buffer[bufferPointer++];
		}

		private int readOutSpaces() throws IOException {
			while (true) {
				if (bufferPointer == bytesRead) fillBuffer();
				int c = buffer[bufferPointer++];
				if (!isSpaceChar(c)) {
					return c;
				}
			}
		}

		public void close() throws IOException {
			if (din == null) return;
			din.close();
		}
	}

}