Problem: You are given a string s, consisting only of characters '0' or '1'. Let |s| be the length of s.

You are asked to choose some integer k (k > 0) and find a sequence a of length k such that: 

  * 1 ≤ a_1 < a_2 < ... < a_k ≤ |s|; 
  * a_{i-1} + 1 < a_i for all i from 2 to k. 



The characters at positions a_1, a_2, ..., a_k are removed, the remaining characters are concatenated without changing the order. So, in other words, the positions in the sequence a should not be adjacent.

Let the resulting string be s'. s' is called sorted if for all i from 2 to |s'| s'_{i-1} ≤ s'_i.

Does there exist such a sequence a that the resulting string s' is sorted?

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of testcases.

Then the descriptions of t testcases follow.

The only line of each testcase contains a string s (2 ≤ |s| ≤ 100). Each character is either '0' or '1'.

Output

For each testcase print "YES" if there exists a sequence a such that removing the characters at positions a_1, a_2, ..., a_k and concatenating the parts without changing the order produces a sorted string.

Otherwise, print "NO".

You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES are all recognized as positive answer).

Example

Input


5
10101011011
0000
11111
110
1100


Output


YES
YES
YES
YES
NO

Note

In the first testcase you can choose a sequence a=[1,3,6,9]. Removing the underlined letters from "10101011011" will produce a string "0011111", which is sorted.

In the second and the third testcases the sequences are already sorted.

In the fourth testcase you can choose a sequence a=[3]. s'= "11", which is sorted.

In the fifth testcase there is no way to choose a sequence a such that s' is sorted.

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.PrintStream;
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.function.Function;
import java.util.stream.Collectors;import java.util.stream.IntStream;import java.util.stream.LongStream;
import java.util.stream.Stream;import static java.lang.System.out;public class _p001499B {
static public void main(final String[] args) throws IOException{p001499B._main(args);}

static class p001499B extends Solver{public p001499B(){}@Override public void solve()throws 
IOException{int[]s=sc.nextLine().chars().toArray();boolean res=true;int cur='1';
for(int i=1;i<s.length;i++){if(s[i]==cur && s[i-1]==cur){if(cur=='1'){cur='0';}else
{res=false;break;}}}out.println(Datas.yesNo(res));}static public void _main(String[]
args)throws IOException{new p001499B().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;}private 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;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();
System.out.flush();}}else{count_tests=1;current_test=1;solve();System.out.flush();
}}private void doNotPreprocessWarning(){System.out.println("/*********************************/");
System.out.println("/* Warning! doNotPreprocess=true */");System.out.println("/* Target file is not compiled!  */");
System.out.println("/*********************************/");}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);
){select_output();done=true;sc=new MyScanner(fis);process();}}else{throw new RuntimeException("File "
+new File(nameIn).getAbsolutePath()+" does not exist!");}}}catch(IOException | AccessControlException 
ex){}if(!done){select_output();sc=new MyScanner(System.in);process();}}private void 
select_output()throws FileNotFoundException{if(nameOut!=null){System.setOut(new 
PrintStream(nameOut));}}}}