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.ByteArrayInputStream;
    import java.io.IOException;
    import java.io.InputStream;
    import java.io.PrintWriter;
    import java.util.Arrays;
    import java.util.InputMismatchException;
     
    public class B {
    	InputStream is;
    	PrintWriter out;
    	String INPUT = "";
    	
    	void solve()
    	{
    		int n = ni();
    		int[] par = new int[n];
    		par[0] = -1;
    		for(int i = 1;i < n;i++){
    			par[i] = ni()-1;
    		}
    		int[][] ch = parentToChildren(par);
    		int[] lc = new int[n];
    		for(int i = 1;i < n;i++){
    			if(ch[i].length == 0){
    				lc[par[i]]++;
    			}
    		}
    		for(int i = 0;i < n;i++){
    			if(ch[i].length > 0){
    				if(lc[i] < 3){
    					out.println("No");
    					return;
    				}
    			}
    		}
    		out.println("Yes");
    	}
    	
    	public static int[][] parentToChildren(int[] par)
    	{
    		int n = par.length;
    		int[] ct = new int[n];
    		for(int i = 0;i < n;i++){
    			if(par[i] >= 0){
    				ct[par[i]]++;
    			}
    		}
    		int[][] g = new int[n][];
    		for(int i = 0;i < n;i++){
    			g[i] = new int[ct[i]];
    		}
    		for(int i = 0;i < n;i++){
    			if(par[i] >= 0){
    				g[par[i]][--ct[par[i]]] = i;
    			}
    		}
    		
    		return g;
    	}
     
    	
    	void run() throws Exception
    	{
    		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
    		out = new PrintWriter(System.out);
    		
    		long s = System.currentTimeMillis();
    		solve();
    		out.flush();
    		tr(System.currentTimeMillis()-s+"ms");
    	}
    	
    	public static void main(String[] args) throws Exception { new B().run(); }
    	
    	private byte[] inbuf = new byte[1024];
    	public int lenbuf = 0, ptrbuf = 0;
    	
    	private int readByte()
    	{
    		if(lenbuf == -1)throw new InputMismatchException();
    		if(ptrbuf >= lenbuf){
    			ptrbuf = 0;
    			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
    			if(lenbuf <= 0)return -1;
    		}
    		return inbuf[ptrbuf++];
    	}
    	
    	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    	
    	private double nd() { return Double.parseDouble(ns()); }
    	private char nc() { return (char)skip(); }
    	
    	private String ns()
    	{
    		int b = skip();
    		StringBuilder sb = new StringBuilder();
    		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
    			sb.appendCodePoint(b);
    			b = readByte();
    		}
    		return sb.toString();
    	}
    	
    	private char[] ns(int n)
    	{
    		char[] buf = new char[n];
    		int b = skip(), p = 0;
    		while(p < n && !(isSpaceChar(b))){
    			buf[p++] = (char)b;
    			b = readByte();
    		}
    		return n == p ? buf : Arrays.copyOf(buf, p);
    	}
    	
    	private char[][] nm(int n, int m)
    	{
    		char[][] map = new char[n][];
    		for(int i = 0;i < n;i++)map[i] = ns(m);
    		return map;
    	}
    	
    	private int[] na(int n)
    	{
    		int[] a = new int[n];
    		for(int i = 0;i < n;i++)a[i] = ni();
    		return a;
    	}
    	
    	private int ni()
    	{
    		int num = 0, b;
    		boolean minus = false;
    		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    		if(b == '-'){
    			minus = true;
    			b = readByte();
    		}
    		
    		while(true){
    			if(b >= '0' && b <= '9'){
    				num = num * 10 + (b - '0');
    			}else{
    				return minus ? -num : num;
    			}
    			b = readByte();
    		}
    	}
    	
    	private long nl()
    	{
    		long num = 0;
    		int b;
    		boolean minus = false;
    		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    		if(b == '-'){
    			minus = true;
    			b = readByte();
    		}
    		
    		while(true){
    			if(b >= '0' && b <= '9'){
    				num = num * 10 + (b - '0');
    			}else{
    				return minus ? -num : num;
    			}
    			b = readByte();
    		}
    	}
    	
    	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
    }