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.math.BigInteger;
	import java.math.RoundingMode;
	import java.text.DecimalFormat;
	import java.util.*;
	
	
	public class Solution
	{
	
		static double eps=(double)1e-6;
		static long mod=(long)(1e9+7);
		//static int arr[] =new int[1000001];
		//private static DecimalFormat df2 = new DecimalFormat(".##");
		public static void main(String args[]){
			InputReader sc = new InputReader(System.in);
			//Scanner sc=new Scanner(System.in);
			OutputStream outputStream = System.out;
			PrintWriter out = new PrintWriter(outputStream);
			//----------my code----------
			int t1=1;
			while(t1-->0)
			{
				int n=sc.nextInt();
				ArrayList<Integer>[] a=new ArrayList[n+1];
				for(int i=1;i<=n;i++)
					a[i]=new ArrayList<Integer>();
				for(int i=2;i<=n;i++)
				{
					a[sc.nextInt()].add(i);
				}
				int flag=0;
				for(int i=1;i<=n;i++)
				{
					if(a[i].size()>0){
						int count=0;
					for(int j=0;j<a[i].size();j++)
					{
						if(a[a[i].get(j)].size()==0)
							count++;
					}
					if(count<3)
					{
						flag=1;
						break;
					}
					}
				}
				if(flag==1)
					out.println("No");
				else
					out.println("Yes");
			}
			//---------------------------------
			out.close();
		}
		
		static int curr_color(int arr[],int i,int curr[])
		{
			if(curr[i]!=0)
				return curr[i];
			return curr_color(arr,arr[i],curr);
		}
		
		static long modInverse(long A,long M)
		{
		    return modularExpon(A,M-2,M);
		}
		
		static long comb(int n,int r,long [][] c)
		{
			if(n<r)
				return 0;
			if(n-r < r) 
			{
				c[n][r]=comb(n,n-r,c);
				return c[n][r];
			}
		    if(r == 0)
		    {
		    	c[n][r]=1;
		    	return 1;
		   	}
		    if(c[n][r]!=0)
		    	return c[n][r];
		    else
		    {
		    	c[n][r]=(n*comb(n-1, r-1,c))/r;
		    	return c[n][r];
		    }
		}
		
		static long modularExpon(long x,long n,long M)
		{
		    long result=1;
		    while(n>0)
		    {
		        if(n % 2 ==1)
		            result=(result * x)%M;
		        x=(x*x)%M;
		        n=n/2;
		    }
		    return result%M;
		}
		
		static int IsPandigital(int n)
	    {
	        int digits = 0,temp=n; int count = 0; int tmp = 0;
	        int fr[]=new int[10];
	        for(int i=0;i<10;i++)
	        	fr[i]=0;
	        while(temp>0)
	        {
	        	int a=temp/10;
	        	//System.out.println(temp-a*10);
	        	fr[temp-a*10]++;
	        	temp=temp/10;
	        	digits++;
	        }
	        for(int i=1;i<=digits;i++)
	        {
	        	if(fr[i]==1)
	        	{
	        		tmp=1;
	        	}
	        	else
	        	{
	        		tmp=0;
	        		break;
	        	}
	        }
	        return tmp;
	    }
		
		static int Divisors(int n)
		{
			int sum=0;
		    for (int i=2; i*i<=n; i++)
		    {
		        if (n%i==0)
		        {
		            if (n/i == i)
		                {sum+=i;//System.out.println(sum+" "+i);
		                }
		 
		            else 
		                {sum+=i+(n/i);//System.out.println(sum+" "+i+" "+(n/i));
		                }
		        }
		    }
		    return sum;
		}
		
		static int findmax(int arr[], int n)
	    {
	        int incl = arr[0];
	        int excl = 0;
	        int excl_new;
	        int i;
	 
	        for (i = 1; i < n; i++)
	        {
	            excl_new = (incl > excl) ? incl : excl;
	            incl = excl + arr[i];
	            excl = excl_new;
	        }
	        return ((incl > excl) ? incl : excl);
	    }
		
		static long ce(long x)
		{
			if(x%2!=0)
				return x/2+1;
			return x/2;
		}
		static boolean isSubSequence(String str1, String str2, int m, int n)
		{
		   int j = 0;
		   for (int i=0; i<n&&j<m; i++)
		       if (str1.charAt(j) == str2.charAt(i))
		         j++;
		 
		   return (j==m);
		}
		
		static long fibo(long l) {
	        if (l < 0) {
	            throw new IllegalArgumentException("The fibo value cannot be negative");
	        }
	
	        if (l <= 1) return l;
	
	        long[][] result = {{1, 0}, {0, 1}}; // identity matrix.
	        long[][] fiboM = {{1, 1}, {1, 0}};
	
	        while (l > 0) {
	            if (l%2 == 1) {
	                multMatrix(result, fiboM);
	            }
	            l = l / 2;
	            multMatrix(fiboM, fiboM);
	        }
	
	        return result[1][0];
	    }
	
	    private static void multMatrix(long[][] result, long[][] fiboM) {
	        long a = (result[0][0]%mod * fiboM[0][0]%mod)%mod +  (result[0][1]%mod * fiboM[1][0]%mod)%mod;
	        long b = (result[0][0]%mod * fiboM[0][1]%mod)%mod + ( result[0][1]%mod * fiboM[1][1]%mod)%mod;
	        long c = (result[1][0]%mod * fiboM[0][0]%mod)%mod + ( result[1][1]%mod * fiboM[0][1]%mod)%mod;
	        long d = (result[1][0]%mod * fiboM[0][1]%mod)%mod +  (result[1][1]%mod * fiboM[1][1]%mod)%mod;
	
	        result[0][0] = a;
	        result[0][1] = b;
	        result[1][0] = c;
	        result[1][1] = d;
	    }
	    
	    static HashSet<Long> gr(int size)
	    {
	    	long range=mod;
	    	long m0=2017;
	    	long m1=2027;
	    	long ln=0;
	    	long sln=1;
	    	long mn=0;
	    	HashSet<Long> hs=new HashSet<Long>();
	    	for(int i=0;i<size;i++)
	    	{
	    		long nn=((((ln%mod)*m0)%mod+((sln%mod)*m1)%mod+mn)%mod)+1;
	    		sln=ln;
	    		ln=nn;
	    		mn=Math.max(mn, nn);
	    		hs.add(nn);
	    	}
	    	return hs;
	    }
	    
		static int[] sieve(int n,int[] a)
		{
			a[0]=1;
			a[1]=1;
			for(int i=2;i*i<=n;i++)
			{
				if(a[i]==0)
				{
					for(int j=i*2;j<=n;j+=i)
						a[j]=1;
				}
			}
			return a;
		}
		
		static int[] spfsieve(int arr[])
		{
			int n=5000000;
			arr[0]=1;
			arr[1]=1;
			for(int i=2;i<=n;i++)
				arr[i]=i;
			for(int i=4;i<=n;i+=2)
				arr[i]=2;
			for(int i=3;i*i<=n;i++)
			{
				if(arr[i]==i)
				{
					for(int j=i*i;j<=n;j+=i)
						if (arr[j]==j)
		                    arr[j] = i;
				}
			}
			return arr;
		}
		
		static boolean isPal(String s)
		{
			for(int i=0, j=s.length()-1;i<=j;i++,j--)
			{
				if(s.charAt(i)!=s.charAt(j)) return false;
			}
			return true;
		}
		public static String rev(String s)
		{
			StringBuilder sb=new StringBuilder(s);
			sb.reverse();
			return sb.toString();
		}
		    
		static long lcm(long a, long b)
		{
			long temp1=a,temp2=b;
		    return ((a * b) / gcd(temp1, temp2));
		}
		
		static long gcd(long a, long b)
		{
		    if (b==0)
		        return a;
		    return gcd(b, a%b);
		}
		static long modulo(long a,long b,long c) {
			long x=1;
			long y=a;
			while(b > 0){
				if(b%2 == 1){
					x=(x*y)%c;
				}
				y = (y*y)%c; // squaring the base
				b /= 2;
			}
			return  x%c;
		}
		public static void debug(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
		
		static class SegmentTree 
		{
		    long st[]; 
		    public SegmentTree(long arr[], int n)
		    {
		        int x = (int) (Math.ceil(Math.log(n) / Math.log(2)));
		 
		        int max_size = 2 * (int) Math.pow(2, x) - 1;
		 
		        st = new long[max_size];
		 
		        constructSTUtil(arr, 0, n - 1, 0);
		    }
		    int getMid(int s, int e) {
		        return s + (e - s) / 2;
		    }
		 
		    long getSumUtil(int ss, int se, int qs, int qe, int si)
		    {
		        if (qs <= ss && qe >= se)
		            return st[si];
		        if (se < qs || ss > qe)
		            return 0;
		        int mid = getMid(ss, se);
		        return getSumUtil(ss, mid, qs, qe, 2 * si + 1) +
		                getSumUtil(mid + 1, se, qs, qe, 2 * si + 2);
		    }
		 
		    void updateValueUtil(int ss, int se, int i, int diff, int si)
		    {
		        if (i < ss || i > se)
		            return;
		        st[si] = st[si] + diff;
		        if (se != ss) {
		            int mid = getMid(ss, se);
		            updateValueUtil(ss, mid, i, diff, 2 * si + 1);
		            updateValueUtil(mid + 1, se, i, diff, 2 * si + 2);
		        }
		    }
		 
		    void updateValue(int arr[], int n, int i, int new_val)
		    {
		        if (i < 0 || i > n - 1) {
		            System.out.println("Invalid Input");
		            return;
		        }
		 
		        // Get the difference between new value and old value
		        int diff = new_val - arr[i];
		 
		        // Update the value in array
		        arr[i] = new_val;
		 
		        // Update the values of nodes in segment tree
		        updateValueUtil(0, n - 1, i, diff, 0);
		    }
		    long getSum(int n, int qs, int qe)
		    {
		        if (qs < 0 || qe > n - 1 || qs > qe) {
		            System.out.println("Invalid Input");
		            return -1;
		        }
		        return getSumUtil(0, n - 1, qs, qe, 0);
		    }
		 
		    long constructSTUtil(long arr[], int ss, int se, int si)
		    {
		        if (ss == se) {
		            st[si] = arr[ss];
		            return arr[ss];
		        }
		        int mid = getMid(ss, se);
		        st[si] = constructSTUtil(arr, ss, mid, si * 2 + 1) +
		                 constructSTUtil(arr, mid + 1, se, si * 2 + 2);
		        return st[si];
		    }
		}
		static class Pair {
			long x;
			long y;
			/*Pair(int xx,int yy,int zz){
				x=xx;
				y=yy;
				z=zz;
			}*/
			public long getx()
			{
				return x;
			}
			public long gety()
			{
				return y;
			}
			public void setx(long xx)
			{
				x=xx;
			}
			public void sety(long yy)
			{
				y=yy;
			}
		}
		
		public final static Comparator<Pair> ORIGINAL = new Comparator<Pair>()
	    {
		public int compare(Pair p1,Pair p2)
		{
			if(p1.getx()<p2.getx())
				return -1;
			else if(p1.getx()==p2.getx() && p1.gety()<p2.gety())
				return -1;
			else //if(p1.getx()>p2.getx() || p1.gety()>p2.gety() || p1.getz()>p2.getz())
				return 1;
			/*else
			{
				if(p1.gety()<p2.gety())
					return -1;
				else if(p1.gety()>p2.gety())
					return 1;
				else
				{
					if(p1.getz()<p2.getz())
						return -1;
					else if(p1.getz()>p2.getz())
						return 1;
				}
			}*/
			//return 0;
		}
	    };
		
		static class InputReader {
			public BufferedReader reader;
			public StringTokenizer tokenizer;
	
			public InputReader(InputStream inputstream) {
				reader = new BufferedReader(new InputStreamReader(inputstream));
				tokenizer = null;
			}
	
			public String nextLine(){
				String fullLine=null;
				while (tokenizer == null || !tokenizer.hasMoreTokens()) {
					try {
						fullLine=reader.readLine();
					} catch (IOException e) {
						throw new RuntimeException(e);
					}
					return fullLine;
				}
				return fullLine;
			}
			public String next() {
				while (tokenizer == null || !tokenizer.hasMoreTokens()) {
					try {
						tokenizer = new StringTokenizer(reader.readLine());
					} catch (IOException e) {
						throw new RuntimeException(e);
					}
				}
				return tokenizer.nextToken();
			}
			public long nextLong() {
				return Long.parseLong(next());
			}
			public int nextInt() {
				return Integer.parseInt(next());
			}
		}
		
	}
	class Graph
	{
		int vertices;
		LinkedList<Integer> l[];
		Graph(int vertices)
		{
			this.vertices=vertices;
			l=new LinkedList[vertices];
			for(int i=0;i<vertices;i++)
			{
				l[i]=new LinkedList<Integer>();
			}
		}	
		void addEdge(int s,int v)
		{
			l[s].add(v);
		}
		
		void BFS(int s)
		{
			LinkedList<Integer> queue=new LinkedList<Integer>();
			boolean []visited=new boolean[vertices];
			visited[s]=true;
			queue.add(s);
			while(queue.size()>0)
			{
				int r=queue.poll();
				System.out.println(r+" ");
				for(int i=0;i<l[r].size();i++)
				{
					int temp=l[r].get(i);
					if(!visited[temp])
					{
						queue.add(temp);
						visited[temp]=true;
					}
				}
			}
		}
		
	}