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.BufferedOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.util.InputMismatchException;
public class A
{
    public static void solve()
    {
        int t=sc.nextInt();
        while (t-->0)
        {
           String str = sc.next();
           int n = str.length();
           boolean flag = false;
           int temp = 0;
           for (int i=n-1;i>0;i--) {
        	   if (str.charAt(i)=='0' && str.charAt(i-1)=='0') {
        		   temp = i-1;
        		   flag = true;
        		   break;
        	   }
           }
           if (!flag) {
        	   out.println("YES");
           }
           else {
        	   boolean flag1 = false;
        	   for (int i=temp;i>0;i--) {
        		   if (str.charAt(i)==str.charAt(i-1) && str.charAt(i)=='1') {
        			   flag1 = true;
        			   break;
        		   }
        	   }
        	   if (!flag1) out.println("YES");
        	   else out.println("NO");
           }
        }
    }
    public static void main(String[] args) 
    {
        new Thread(null, null, "Thread", 1 << 27) 
        {
            public void run() 
            {
                try 
                {
                    out = new PrintWriter(new BufferedOutputStream(System.out));
                    sc = new FastReader(System.in);
                    solve();
                    out.close();
                } 
                catch (Exception e) 
                {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }
                .start();
    }
    public static int[] arrprime(int[] prime) {
    	prime[0] = 1;
    	prime[1] = 2;
    	int num = 3;
    	boolean flag = true;
    	for (int i=2;i<1501;) {
    		for (int j=2;j<=Math.sqrt(num);j++) {
    			if (num%j==0) {
    				flag = false;
    				break;
    			}
    			
    		}
    		if (flag) {
    			prime[i] = num;
    			i++;
    		}
    		num++;
    		flag = true;
    	}
    	return prime;
    }
    public static class Pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<Pair<U, V>> 
    {
        public U x;
        public V y;
    
        public Pair(U x, V y) 
        {
            this.x = x;
            this.y = y;
        }
    
        public int hashCode() 
        {
            return (x == null ? 0 : x.hashCode() * 31) + (y == null ? 0 : y.hashCode());
        }
    
        public boolean equals(Object o) 
        {
            if (this == o)
                return true;
            if (o == null || getClass() != o.getClass())
                return false;
            Pair<U, V> p = (Pair<U, V>) o;
            return (x == null ? p.x == null : x.equals(p.x)) && (y == null ? p.y == null : y.equals(p.y));
        }
    
        public int compareTo(Pair<U, V> b) {
            int cmpU = x.compareTo(b.x);
            return cmpU != 0 ? cmpU : y.compareTo(b.y);
        }
    
        public String toString() {
            return String.format("(%s, %s)", x.toString(), y.toString());
        }
    
    }
    static final Random random=new Random();
    static int max(int[] arr)
    {
    	int m=Integer.MIN_VALUE;
    	for (int i=0;i<arr.length;i++)
    	{
    		m=Math.max(arr[i], m);
    	}
    	return m;
    }
    static int min(int[] arr)
    {
    	int m=Integer.MAX_VALUE;
    	for (int i=0;i<arr.length;i++)
    	{
    		m=Math.min(arr[i], m);
    	}
    	return m;
    }
    static int gcd(int a,int b)
    {
        if (b==a)
            return a;
        return gcd(b,a%b);
    }
    static void UjjRevSort(int[] a) 
    {
        ArrayList<Integer> arr = new ArrayList(a.length);
        for (int i=0;i<a.length;i++) {
        	arr.add(i, a[i]);
        }
        Collections.sort(arr,Collections.reverseOrder());
        for (int i=0;i<arr.size();i++) {
        	a[i] = arr.get(i);
        }
        
    }
    static void UjjwalSort(int[] a) 
    {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) 
        {
            int ujjwal=random.nextInt(n), temp=a[ujjwal];
            a[ujjwal]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
    public static PrintWriter out;
    public static FastReader sc;
    public static class FastReader 
    {
        private InputStream stream;
        private byte[] buf = new byte[4096];
        private int curChar, snumChars;
        public FastReader(InputStream stream) 
        {
            this.stream = stream;
        }
        public int read() 
        {
            if (snumChars == -1) 
            {
                throw new InputMismatchException();
            }
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                catch (IOException E) 
                {
                    throw new InputMismatchException();
                }
            }
            if (snumChars <= 0) 
            {
                return -1;
            }
            return buf[curChar++];
        }
        public int nextInt() 
        {
            int c = read();
            while (isSpaceChar(c)) 
            {
                c = read();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            int number = 0;
            do 
            {
                number *= 10;
                number += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return number * sgn;
        }
        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) 
            {
                c = read();
            }
            long sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            long number = 0;
            do 
            {
                number *= 10L;
                number += (long) (c - '0');
                c = read();
            } while (!isSpaceChar(c));
            return number * sgn;
        }
        public int[] nextIntArray(int n) 
        {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) 
            {
                arr[i] = this.nextInt();
            }
            return arr;
        }
        public long[] nextLongArray(int n) 
        {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) 
            {
                arr[i] = this.nextLong();
            }
            return arr;
        }
        public String next()
        {
            int c = read();
            while (isSpaceChar(c)) 
            {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
        public String nextLine() 
        {
            int c = read();
            while (isSpaceChar(c)) 
            {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();	
            } while (!isEndofLine(c));
            return res.toString();
        }
        public boolean isSpaceChar(int c)
        {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
        public boolean isEndofLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
}