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.File;import java.io.FileInputStream;import java.io.FileNotFoundException;
import java.io.IOException;import java.io.InputStream;import java.io.PrintWriter;
import java.lang.annotation.Retention;import java.lang.annotation.RetentionPolicy;
import java.lang.reflect.Array;import java.lang.reflect.Field;import java.lang.reflect.InvocationTargetException;
import java.lang.reflect.Method;import java.security.AccessControlException;import java.util.Arrays;
import java.util.Collection;import java.util.Comparator;import java.util.List;import java.util.Map;
import java.util.Objects;import java.util.TreeMap;import java.util.TreeSet;import java.util.function.Function;
import java.util.stream.Collectors;import java.util.stream.IntStream;import java.util.stream.LongStream;
import java.util.stream.Stream;public class _p000913B {static public void main(final String[] args) 
throws IOException{p000913B._main(args);}
static class p000913B extends Solver{public p000913B(){singleTest=true;}@Override public 
void solve()throws IOException{int n=sc.nextInt();sc.nextLine();int[]p=new int[n
-1];for(int $i0=0;$i0<n-1;$i0++){p[$i0]=sc.nextInt();sc.nextLine();}TreeSet<Integer>
parents=new TreeSet<>();parents.addAll(Datas.list(p));TreeSet<int[]>set=new TreeSet<>((x,
y)->x[0]!=y[0]?x[0]-y[0]:x[1]-y[1]);set.addAll(Datas.listi(p));boolean res=true;int cur
=0;int prev=-1;while(!set.isEmpty()){int[]it=set.pollFirst();if(prev!=-1){if(prev
!=it[0]){if(cur<3){res=false;break;}cur=0;}}if(!parents.contains(it[1]+2)){cur++;
}prev=it[0];}if(cur<3){res=false;}pw.println(res?"Yes":"No");}static public void 
_main(String[]args)throws IOException{new p000913B().run();}}static class Datas{static 
class Pair<K,V>{private K k;private V v;public Pair(final K t,final V u){this.k=
t;this.v=u;}public K getKey(){return k;}public V getValue(){return v;}}final static 
String SPACE=" ";public static TreeMap<Integer,Integer>mapc(final int[]a){return 
IntStream.range(0,a.length).collect(()->new TreeMap<Integer,Integer>(),(res,i)->
{res.put(a[i],res.getOrDefault(a[i],0)+1);},Map::putAll);}public static TreeMap<Long,
Integer>mapc(final long[]a){return IntStream.range(0,a.length).collect(()->new TreeMap<Long,
Integer>(),(res,i)->{res.put(a[i],res.getOrDefault(a[i],0)+1);},Map::putAll);}public 
static<T>TreeMap<T,Integer>mapc(final T[]a,Comparator<T>cmp){return IntStream.range(0,
a.length).collect(cmp!=null?()->new TreeMap<T,Integer>(cmp):()->new TreeMap<T,Integer>(),
(res,i)->{res.put(a[i],res.getOrDefault(a[i],0)+1);},Map::putAll);}public static
<T>TreeMap<T,Integer>mapc(final T[]a){return mapc(a,null);}public static TreeMap<Integer,
Integer>mapc(final IntStream a){return a.collect(()->new TreeMap<Integer,Integer>(),
(res,v)->{res.put(v,res.getOrDefault(v,0)+1);},Map::putAll);}public static TreeMap<Long,
Integer>mapc(final LongStream a){return a.collect(()->new TreeMap<Long,Integer>(),
(res,v)->{res.put(v,res.getOrDefault(v,0)+1);},Map::putAll);}public static<T>TreeMap<T,
Integer>mapc(final Stream<T>a,Comparator<T>cmp){return a.collect(cmp!=null?()->new 
TreeMap<T,Integer>(cmp):()->new TreeMap<T,Integer>(),(res,v)->{res.put(v,res.getOrDefault(v,
0)+1);},Map::putAll);}public static<T>TreeMap<T,Integer>mapc(final Stream<T>a){return 
mapc(a,null);}public static<T>TreeMap<T,Integer>mapc(final Collection<T>a,Comparator<T>
cmp){return mapc(a.stream(),cmp);}public static<T>TreeMap<T,Integer>mapc(final Collection<T>
a){return mapc(a.stream());}public static TreeMap<Integer,List<Integer>>mapi(final 
int[]a){return IntStream.range(0,a.length).collect(()->new TreeMap<Integer,List<Integer>>(),
(res,i)->{if(!res.containsKey(a[i])){res.put(a[i],Stream.of(i).collect(Collectors.toList()));
}else{res.get(a[i]).add(i);}},Map::putAll);}public static TreeMap<Long,List<Integer>>
mapi(final long[]a){return IntStream.range(0,a.length).collect(()->new TreeMap<Long,
List<Integer>>(),(res,i)->{if(!res.containsKey(a[i])){res.put(a[i],Stream.of(i).collect(Collectors.toList()));
}else{res.get(a[i]).add(i);}},Map::putAll);}public static<T>TreeMap<T,List<Integer>>
mapi(final T[]a,Comparator<T>cmp){return IntStream.range(0,a.length).collect(cmp
!=null?()->new TreeMap<T,List<Integer>>(cmp):()->new TreeMap<T,List<Integer>>(),
(res,i)->{if(!res.containsKey(a[i])){res.put(a[i],Stream.of(i).collect(Collectors.toList()));
}else{res.get(a[i]).add(i);}},Map::putAll);}public static<T>TreeMap<T,List<Integer>>
mapi(final T[]a){return mapi(a,null);}public static TreeMap<Integer,List<Integer>>
mapi(final IntStream a){int[]i=new int[]{0};return a.collect(()->new TreeMap<Integer,
List<Integer>>(),(res,v)->{if(!res.containsKey(v)){res.put(v,Stream.of(i[0]).collect(Collectors.toList()));
}else{res.get(v).add(i[0]);}i[0]++;},Map::putAll);}public static TreeMap<Long,List<Integer>>
mapi(final LongStream a){int[]i=new int[]{0};return a.collect(()->new TreeMap<Long,
List<Integer>>(),(res,v)->{if(!res.containsKey(v)){res.put(v,Stream.of(i[0]).collect(Collectors.toList()));
}else{res.get(v).add(i[0]);}i[0]++;},Map::putAll);}public static<T>TreeMap<T,List<Integer>>
mapi(final Stream<T>a,Comparator<T>cmp){int[]i=new int[]{0};return a.collect(cmp
!=null?()->new TreeMap<T,List<Integer>>(cmp):()->new TreeMap<T,List<Integer>>(),
(res,v)->{if(!res.containsKey(v)){res.put(v,Stream.of(i[0]).collect(Collectors.toList()));
}else{res.get(v).add(i[0]);}i[0]++;},Map::putAll);}public static<T>TreeMap<T,List<Integer>>
mapi(final Stream<T>a){return mapi(a,null);}public static<T>TreeMap<T,List<Integer>>
mapi(final Collection<T>a,Comparator<T>cmp){return mapi(a.stream(),cmp);}public 
static<T>TreeMap<T,List<Integer>>mapi(final Collection<T>a){return mapi(a.stream());
}public static List<int[]>listi(final int[]a){return IntStream.range(0,a.length).mapToObj(i
->new int[]{a[i],i}).collect(Collectors.toList());}public static List<long[]>listi(final 
long[]a){return IntStream.range(0,a.length).mapToObj(i->new long[]{a[i],i}).collect(Collectors.toList());
}public static<T>List<Pair<T,Integer>>listi(final T[]a){return IntStream.range(0,
a.length).mapToObj(i->new Pair<T,Integer>(a[i],i)).collect(Collectors.toList());
}public static List<int[]>listi(final IntStream a){int[]i=new int[]{0};return a.mapToObj(v
->new int[]{v,i[0]++}).collect(Collectors.toList());}public static List<long[]>listi(final 
LongStream a){int[]i=new int[]{0};return a.mapToObj(v->new long[]{v,i[0]++}).collect(Collectors.toList());
}public static<T>List<Pair<T,Integer>>listi(final Stream<T>a){int[]i=new int[]{0};
return a.map(v->new Pair<T,Integer>(v,i[0]++)).collect(Collectors.toList());}public 
static<T>List<Pair<T,Integer>>listi(final Collection<T>a){int[]i=new int[]{0};return 
a.stream().map(v->new Pair<T,Integer>(v,i[0]++)).collect(Collectors.toList());}public 
static String join(final int[]a){return Arrays.stream(a).mapToObj(Integer::toString).collect(Collectors.joining(SPACE));
}public static String join(final long[]a){return Arrays.stream(a).mapToObj(Long::toString).collect(Collectors.joining(SPACE));
}public static<T>String join(final T[]a){return Arrays.stream(a).map(v->Objects.toString(v)).collect(Collectors.joining(SPACE));
}public static<T>String join(final T[]a,final Function<T,String>toString){return 
Arrays.stream(a).map(v->toString.apply(v)).collect(Collectors.joining(SPACE));}public 
static<T>String join(final Collection<T>a){return a.stream().map(v->Objects.toString(v)).collect(Collectors.joining(SPACE));
}public static<T>String join(final Collection<T>a,final Function<T,String>toString)
{return a.stream().map(v->toString.apply(v)).collect(Collectors.joining(SPACE));
}public static<T>String join(final Stream<T>a){return a.map(v->Objects.toString(v)).collect(Collectors.joining(SPACE));
}public static<T>String join(final Stream<T>a,final Function<T,String>toString){
return a.map(v->toString.apply(v)).collect(Collectors.joining(SPACE));}public static
<T>String join(final IntStream a){return a.mapToObj(Integer::toString).collect(Collectors.joining(SPACE));
}public static<T>String join(final LongStream a){return a.mapToObj(Long::toString).collect(Collectors.joining(SPACE));
}public static List<Integer>list(final int[]a){return Arrays.stream(a).mapToObj(Integer::valueOf).collect(Collectors.toList());
}public static List<Integer>list(final IntStream a){return a.mapToObj(Integer::valueOf).collect(Collectors.toList());
}public static List<Long>list(final long[]a){return Arrays.stream(a).mapToObj(Long::valueOf).collect(Collectors.toList());
}public static List<Long>list(final LongStream a){return a.mapToObj(Long::valueOf).collect(Collectors.toList());
}public static<T>List<T>list(final Stream<T>a){return a.collect(Collectors.toList());
}public static<T>List<T>list(final Collection<T>a){return a.stream().collect(Collectors.toList());
}public static<T>List<T>list(final T[]a){return Arrays.stream(a).collect(Collectors.toList());
}public static String yesNo(final boolean res){return res?"YES":"NO";}public static 
String dump(Object obj){String res="";if(obj!=null){Class cl=obj.getClass();String 
cls=cl.getName();if(cls.startsWith("[")){res+="[";for(int i=0;;i++){try{Object o
=Array.get(obj,i);String s=dump(o);if(i>0){res+=", ";}res+=s;}catch(ArrayIndexOutOfBoundsException 
ex){break;}}res+="]";}else if(Collection.class.isAssignableFrom(cl)){@SuppressWarnings("unchecked")final 
Object s=((Collection)obj).stream().map(v->dump(v)).collect(Collectors.joining(", ",
"[","]"));res+=s.toString();}else if(Map.class.isAssignableFrom(cl)){@SuppressWarnings("unchecked")final 
Object s=((Map)obj).entrySet().stream().map(v->dump(v)).collect(Collectors.joining(", ",
"{","}"));res+=s.toString();}else if(Character.class.isInstance(obj)|| Integer.class.isInstance(obj)
|| Long.class.isInstance(obj)|| Float.class.isInstance(obj)|| Double.class.isInstance(obj)|| String.class.isInstance(obj)
){res+=Objects.toString(obj);}else if(Map.Entry.class.isInstance(obj)){res+=dump(((Map.Entry)obj).getKey())
+"="+dump(((Map.Entry)obj).getValue());}else if(Stream.class.isInstance(obj)){@SuppressWarnings("unchecked")
final Object s=((Stream)obj).map(v->dump(v)).collect(Collectors.joining(", ","[",
"]"));res+=s.toString();}else{res+=Stream.concat(Arrays.stream(obj.getClass().getFields()).map(v
->{String name=v.getName();String val;try{Object o=v.get(obj);if(o!=null && v.isAnnotationPresent(Dump.class))
{Dump an=v.getAnnotation(Dump.class);Class ocl=o.getClass();val="{";for(String fn:an.fields())
{try{Field f=ocl.getField(fn);val+=fn+"="+dump(f.get(o))+", ";}catch(NoSuchFieldException 
nsfex){try{@SuppressWarnings("unchecked")final Method m=ocl.getMethod(fn);val+=fn+"="+dump(m.invoke(o))
+", ";}catch(NoSuchMethodException | IllegalArgumentException | InvocationTargetException 
nsmex){}}}if(val.endsWith(", ")){val=val.substring(0,val.length()-2);}val+="}";}
else{val=dump(o);}}catch(IllegalAccessException ex){val="N/A";}return name+"="+val;
}),Arrays.stream(obj.getClass().getMethods()).filter(m->m.isAnnotationPresent(Getter.class)).map(m
->{String name=m.getName();String val;try{Object o=m.invoke(obj);if(o!=null && m.isAnnotationPresent(Dump.class))
{Dump an=m.getAnnotation(Dump.class);Class ocl=o.getClass();val="{";for(String fn:an.fields())
{try{Field f=ocl.getField(fn);val+=fn+"="+dump(f.get(o))+", ";}catch(NoSuchFieldException 
nsfex){try{@SuppressWarnings("unchecked")final Method m1=ocl.getMethod(fn);val+=fn+"="+dump(m1.invoke(o))
+", ";}catch(NoSuchMethodException | IllegalArgumentException | InvocationTargetException 
nsmex){}}}if(val.endsWith(", ")){val=val.substring(0,val.length()-2);}val+="}";}else
{val=dump(o);}}catch(IllegalAccessException | InvocationTargetException ex){val=
"N/A";}return name+"="+val;})).collect(Collectors.joining(", ","{"+obj.getClass().getName()
+": ","}"));}}if(res.length()==0){res="<null>";}return res;}}@Retention(RetentionPolicy.RUNTIME)
public @interface Dump{String[]fields();}@Retention(RetentionPolicy.RUNTIME)public @interface Getter{}static class 
MyScanner{private StringBuilder cache=new StringBuilder();int cache_pos=0;private 
int first_linebreak=-1;private int second_linebreak=-1;private StringBuilder sb=
new StringBuilder();private InputStream is=null;public MyScanner(final InputStream 
is){this.is=is;}public String charToString(final int c){return String.format("'%s'",
c=='\n'?"\\n":(c=='\r'?"\\r":String.valueOf((char)c)));}public int get(){int res
=-1;if(cache_pos<cache.length()){res=cache.charAt(cache_pos);cache_pos++;if(cache_pos
==cache.length()){cache.delete(0,cache_pos);cache_pos=0;}}else{try{res=is.read();
}catch(IOException ex){throw new RuntimeException(ex);}}return res;}private void 
unget(final int c){if(cache_pos==0){cache.insert(0,(char)c);}else{cache_pos--;}}
public String nextLine(){sb.delete(0,sb.length());int c;boolean done=false;boolean 
end=false;while((c=get())!=-1){if(check_linebreak(c)){done=true;if(c==first_linebreak)
{if(!end){end=true;}else{cache.append((char)c);break;}}else if(second_linebreak!=
-1 && c==second_linebreak){break;}}if(end && c!=first_linebreak && c!=second_linebreak)
{cache.append((char)c);break;}if(!done){sb.append((char)c);}}return sb.toString();
}private boolean check_linebreak(int c){if(c=='\n'|| c=='\r'){if(first_linebreak
==-1){first_linebreak=c;}else if(c!=first_linebreak && second_linebreak==-1){second_linebreak
=c;}return true;}return false;}public int nextInt(){return Integer.parseInt(next());
}public long nextLong(){return Long.parseLong(next());}public boolean hasNext(){
boolean res=false;int c;while((c=get())!=-1){if(!check_linebreak(c)&& c!=' '&& c
!='\t'){res=true;unget(c);break;}}return res;}public String next(){sb.delete(0,sb.length());
boolean started=false;int c;while((c=get())!=-1){if(check_linebreak(c)|| c==' '|| 
c=='\t'){if(started){unget(c);break;}}else{started=true;sb.append((char)c);}}return 
sb.toString();}public int nextChar(){return get();}public boolean eof(){int c=get();
boolean res=false;if(c!=-1){unget(c);}else{res=true;}return res;}public double nextDouble()
{return Double.parseDouble(next());}}static abstract class Solver{protected String 
nameIn=null;protected String nameOut=null;protected boolean singleTest=false;protected 
MyScanner sc=null;protected PrintWriter pw=null;private int current_test=0;private 
int count_tests=0;protected int currentTest(){return current_test;}protected int 
countTests(){return count_tests;}private void process()throws IOException{if(!singleTest)
{count_tests=sc.nextInt();sc.nextLine();for(current_test=1;current_test<=count_tests;
current_test++){solve();pw.flush();}}else{count_tests=1;current_test=1;solve();}
}abstract protected void solve()throws IOException;public void run()throws IOException
{boolean done=false;try{if(nameIn!=null){if(new File(nameIn).exists()){try(FileInputStream 
fis=new FileInputStream(nameIn);PrintWriter pw0=select_output();){select_output();
done=true;sc=new MyScanner(fis);pw=pw0;process();}}else{throw new RuntimeException("File "
+new File(nameIn).getAbsolutePath()+" does not exist!");}}}catch(IOException | AccessControlException 
ex){}if(!done){try(PrintWriter pw0=select_output();){sc=new MyScanner(System.in);
pw=pw0;process();}}}private PrintWriter select_output()throws FileNotFoundException
{if(nameOut!=null){return new PrintWriter(nameOut);}return new PrintWriter(System.out);
}}}