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:


    //------------------>>>>>>>>>>>>>>>> HI . HOW ARE YOU? <<<<<<<<<<<<<<<<<<<<<<<<<<<<<------------------------------

import java.util.*;
import java.math.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

     //--------------->>>>IF YOU ARE HERE FOR QUICKSORT HACK THEN SORRY NO HACK FOR YOU<<<-------------------

public class a{ 
     static long[] count,count1,count2;
     static boolean[] prime;
     static int[] spf;
     static Node[] nodes,nodes1,nodes2;
     static NodeInt[] nodesInt,nodesInt1;
     static long[] arr;
     static long[][] cost;
     static int[] arrInt,darrInt,farrInt;
     static long[][] dp;
     static char[] ch,ch1;
     static long[] darr,farr;
     static long[][] mat,mat1;
     static boolean[] vis;
     static long x,h;
     static long maxl;
     static double dec;
     static long mx = (long)1e7;
     static long inf = (long)1e15;
     static String s,s1,s2,s3,s4;
     static long minl;   
     static long mod = ((long)(1e9))+7;
     // static int minl = -1;
     // static long n;
     static int n,n1,n2,q,r1,c1,r2,c2;
     static int arr_size = (int)2e5+10;
     static long a;
     static long b;
     static long c;
     static long d;
     static long y,z;
     static int m;
     static int ans;
     static long k;
     static FastScanner sc;
     static String[] str,str1;
     static Set<String> set,set1,set2;
     static SortedSet<Long> ss;
     static List<Integer> list,list1,list2,list3;
     static PriorityQueue<Node> pq,pq1;
     static LinkedList<Node> ll,ll1,ll2;
     static Map<Integer,List<Integer>> map2;
     static Map<Integer,Integer> map;
     static Map<Integer,Node> map1;
     static StringBuilder sb,sb1,sb2;
     static int index;
     static long[] sum;
     static int[] dx = {0,-1,0,1,-1,1,-1,1};
     static int[] dy = {-1,0,1,0,-1,-1,1,1};

     // public static void solve(){

     //    FastScanner sc = new FastScanner();
     //    // int t = sc.nextInt();
     //    int t = 1;
     //    for(int tt = 0 ; tt < t ; tt++){

     //        // s = sc.next();
     //        // s1 = sc.next();

     //        n = sc.nextInt();

     //        m = sc.nextInt();

     //        // int k = sc.nextInt();

     //        // sb = new StringBuilder();

     //        map = new HashMap<>();
     //        map1 = new HashMap<>();

     //        // q = sc.nextInt();
     //        // sb = new StringBuilder();
     //        // long k = sc.nextLong();

     //        // ch = sc.next().toCharArray();

     //        // count = new int[200002];
           
     //        // m = sc.nextInt();

     //        for(int o = 0 ; o < m ; o++){

     //            int l = sc.nextInt()-1;
     //            int r = sc.nextInt()-1;

     //        }

     //    }
        
     // }

     //--------------->>>>IF YOU ARE HERE FOR QUICKSORT HACK THEN SORRY NO HACK FOR YOU<<<--------------------

     public static void solve(){

        int n = ch.length;
        for(int i = 0 ; i < n-1 ; i++){
            if(ch[i] == ch[i+1] && ch[i] == '1'){
                for(int j = i+2 ; j < n-1 ; j++){
                    if(ch[j] == ch[j+1] && ch[j] == '0'){
                        System.out.println("NO");
                        return;
                    }
                }
            }
        }

        System.out.println("YES");

     }

        
     public static void main(String[] args) {

            sc = new FastScanner();
            // Scanner sc = new Scanner(System.in);
            int t = sc.nextInt();
            // int t = 1;
            // int l = 1;
            while(t > 0){
                
                // n = sc.nextInt();
                // n = sc.nextLong();
                // k = sc.nextLong();
                // x = sc.nextLong();
                // y = sc.nextLong();
                // z = sc.nextLong();

                // a = sc.nextLong();
                // b = sc.nextLong();
                // c = sc.nextLong();
                // d = sc.nextLong();

                // x = sc.nextLong();
                // y = sc.nextLong();
                // z = sc.nextLong();
                // d = sc.nextLong();

                // n = sc.nextInt();

                // n1 = sc.nextInt();

                // m = sc.nextInt();
                // q = sc.nextInt();

                // a = sc.nextLong();
                // b = sc.nextLong();

                // k = sc.nextLong();

                // x = sc.nextLong();
                // d = sc.nextLong();

                // s = sc.next();

                ch = sc.next().toCharArray();
                // ch1 = sc.next().toCharArray();

                // m = sc.nextInt();
                // n = 6;

                // arr = new long[n+1];
                // for(int i = 1 ; i <= n ; i++){
                //     arr[i] = sc.nextLong();
                // }

                // arrInt = new int[n];
                // for(int i = 0 ; i < n ; i++){
                //     arrInt[i] = sc.nextInt();
                // }
                // x = sc.nextLong();
                // y = sc.nextLong();
                // ch = sc.next().toCharArray();
                // m = n;
                // m = sc.nextInt();
                // darr = new long[m];
                // for(int i = 0 ; i < m ; i++){
                //     darr[i] = sc.nextLong();
                // }
                // k = sc.nextLong();
                // m = n;
                // darrInt = new int[n];
                // for(int i = 0 ; i < n ; i++){
                //     darrInt[i] = sc.nextInt();
                // }

                // farrInt = new int[m];
                // for(int i = 0; i < m ; i++){
                //     farrInt[i] = sc.nextInt();
                // }

                // m = n;
                // mat = new long[n+1][m+1];
                // for(int i = 1 ; i <= n ; i++){
                //     for(int j = 1 ; j <= m ; j++){
                //         mat[i][j] = sc.nextLong();
                //     }
                // }

                // m = n;
                // mat = new char[n][m];
                // for(int i = 0 ; i < n ; i++){
                //     String s = sc.next();
                //     for(int j = 0 ; j < m ; j++){
                //         mat[i][j] = s.charAt(j);
                //     }
                // }

                // str = new String[n];
                // for(int i = 0 ; i < n ; i++)
                //     str[i] = sc.next();

                // nodes = new Node[n];
                // for(int i = 0 ; i < n ;i++)
                //     nodes[i] = new Node(sc.nextLong(),sc.nextLong());

                // nodesInt = new NodeInt[n];
                // for(int i = 0 ; i < n ;i++)
                //     nodesInt[i] = new NodeInt(sc.nextInt(),sc.nextInt(),i);

                 solve();       
                 t -= 1;
            }

     }

    public static int log(long n,long base){

         if(n == 0 || n == 1)
             return 0;

         if(n == base)
             return 1;

         double num = Math.log(n);
         double den = Math.log(base);

         if(den == 0)
             return 0;

         return (int)(num/den);
     }

    public static boolean isPrime(long n) { 
    // Corner cases 
        if (n <= 1)  
            return false; 

        if (n <= 3)  
            return true; 
      
        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n%2 == 0 || n%3 == 0) 
            return false; 
      
        for (int i=5; i*i<=n; i=i+6) 
            if (n%i == 0 || n%(i+2) == 0) 
               return false; 
      
        return true; 
    } 

    public static void SpecialSieve(int MAXN) 
    {   
        spf = new int[MAXN];
        spf[1] = 1; 
        for (int i=2; i<MAXN; i++) 
       
            // marking smallest prime factor for every 
            // number to be itself. 
            spf[i] = i; 
       
        // separately marking spf for every even 
        // number as 2 
        for (int i=4; i<MAXN; i+=2) 
            spf[i] = 2; 
       
        for (int i=3; i*i<MAXN; i++) 
        { 
            // checking if i is prime 
            if (spf[i] == i) 
            { 
                // marking SPF for all numbers divisible by i 
                for (int j=i*i; j<MAXN; j+=i) 
       
                    // marking spf[j] if it is not  
                    // previously marked 
                    if (spf[j]==j) 
                        spf[j] = i; 
            } 
        } 
    } 

    public static ArrayList<Integer> getFactorization(int x) 
    { 
        ArrayList<Integer> ret = new ArrayList<Integer>(); 
        while (x != 1) 
        { 
            ret.add(spf[x]); 
            x = x / spf[x]; 
        } 
        return ret; 
    } 


    public static long gcd(long a, long b)
    {
      if (b == 0)
        return a;
      return gcd(b, a % b); 
    }

    public static long lcm(long a, long b)
    {
      return (b/gcd(b, a % b)) * a; 
    }

     public static long mod_inverse(long a,long mod){
        long x1=1,x2=0;
        long p=mod,q,t;
        while(a%p!=0){
          q = a/p;
          t = x1-q*x2;
          x1=x2; x2=t;
          t=a%p;
          a=p; p=t;
        }
        return x2<0 ? x2+mod : x2;
    }

     public static void swap(long[] curr,int i,int j){
         long temp = curr[j];
         curr[j] = curr[i];
         curr[i] = temp;
     }

    static final Random random=new Random();

    static void ruffleSortLong(long[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            long temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static void ruffleSortInt(int[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            int temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
    
    static void ruffleSortChar(char[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            char temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static long binomialCoeff(long n, long k){ 

        long res = 1; 
  
        // Since C(n, k) = C(n, n-k) 
        if (k > n - k) 
            k = n - k; 
  
        // Calculate value of 
        // [n * (n-1) *---* (n-k+1)] / [k * (k-1) *----* 1] 
        for (long i = 0; i < k; ++i) { 
            res = (res*(n - i)); 
            res = (res/(i + 1)); 
        } 

        return res; 
    } 

    static long[] fact;

    public static long inv(long n){
        return power(n, mod-2);
    }

    public static void fact(int n){
        fact = new long[n+1];
        fact[0] = 1;
        for(int j = 1;j<=n;j++)
            fact[j] = (fact[j-1]*(long)j)%mod;               
    }

    public static long binom(int n, int k){
        fact(n+1);
        long prod = fact[n];
        prod*=inv(fact[n-k]);
        prod%=mod;
        prod*=inv(fact[k]);
        prod%=mod;
        return prod;    
    }

    static long power(long x, long y){
        if (y == 0)
            return 1;
        if (y%2 == 1)
            return (x*power(x, y-1))%mod;
        return power((x*x)%mod, y/2)%mod;
    }

    public static long pow(long n,long p,long m){
     long  result = 1;
      if(p==0)
        return 1;
          
    while(p!=0)
    {
        if(p%2==1)
            result *= n;
        if(result>=m)
        result%=m;
        p >>=1;
        n*=n;
        if(n>=m)
        n%=m;
    }
    return result;
    }

    static void sieve(int n){ 

        prime = new boolean[n+1]; 
        for(int i=2;i<n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p*p <=n; p++) 
        { 
            if(prime[p] == true) 
            { 
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 

    }

    static class Node{
        long first;
        int second;
        Node(long f,int s){
            this.first = f;
            this.second = s;
        }
    }

    static class NodeInt{
        int first;
        int second;
        int third;
        NodeInt(int f,int s,int third){
            this.first = f;
            this.second = s;
            this.third = third;
        }
    }

    static long abs(long a){
        return Math.abs(a);
    }

    static int abs(int a){
        return Math.abs(a);
    }

    static int max(int a,int b){
    if(a>b)
            return a;
    else
            return b;
    }
 
    static int min(int a,int b){
    if(a>b)
            return b;
    else 
            return a;
    }
 
    static long max(long a,long b){
    if(a>b)
            return a;
    else
            return b;
    }
 
    static long min(long a,long b){
    if(a>b)
            return b;
    else 
            return a;
    }

    static long sq(long num){
        return num*num;
    }

    static double sq(double num){
        return num*num;
    }

    static long sqrt(long num){
        return (long)Math.sqrt(num);
    }

    static double sqrt(double num){
        return Math.sqrt(num);
    }

     static class FastScanner {

                BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                StringTokenizer st=new StringTokenizer("");
                String next() {
                        while (!st.hasMoreTokens())
                                try {
                                        st=new StringTokenizer(br.readLine());
                                } catch (IOException e) {
                                        e.printStackTrace();
                                }
                        return st.nextToken();
                }
                
                int nextInt() {
                        return Integer.parseInt(next());
                }
                int[] readArray(int n) {
                        int[] a=new int[n];
                        for (int i=0; i<n; i++) a[i]=nextInt();
                        return a;
                }
                long nextLong() {
                        return Long.parseLong(next());
                }
        }

}