Problem: Let's say string s has period k if s_i = s_{i + k} for all i from 1 to |s| - k (|s| means length of string s) and k is the minimum positive integer with this property.

Some examples of a period: for s="0101" the period is k=2, for s="0000" the period is k=1, for s="010" the period is k=2, for s="0011" the period is k=4.

You are given string t consisting only of 0's and 1's and you need to find such string s that:

  1. String s consists only of 0's and 1's; 
  2. The length of s doesn't exceed 2 ⋅ |t|; 
  3. String t is a subsequence of string s; 
  4. String s has smallest possible period among all strings that meet conditions 1—3. 



Let us recall that t is a subsequence of s if t can be derived from s by deleting zero or more elements (any) without changing the order of the remaining elements. For example, t="011" is a subsequence of s="10101".

Input

The first line contains single integer T (1 ≤ T ≤ 100) — the number of test cases.

Next T lines contain test cases — one per line. Each line contains string t (1 ≤ |t| ≤ 100) consisting only of 0's and 1's.

Output

Print one string for each test case — string s you needed to find. If there are multiple solutions print any one of them.

Example

Input


4
00
01
111
110


Output


00
01
11111
1010

Note

In the first and second test cases, s = t since it's already one of the optimal solutions. Answers have periods equal to 1 and 2, respectively.

In the third test case, there are shorter optimal solutions, but it's okay since we don't need to minimize the string s. String s has period equal to 1.

Solution (in JAVA):

Solution:
/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;

public class GFG {
	public static void main (String[] args) {
// 		System.out.println("GfG!");
        Scanner in=new Scanner(System.in);
        int t=in.nextInt();
        while(t-->0)
        {
            String g=in.next();
            int c0=0,c11=0;
            for(int i=0;i<g.length();i++)
            {
                char c=g.charAt(i);
                if(c=='0')
                c0++;
                else
                c11++;
            }
            if(c0==0||c11==0)
            {
                System.out.println(g);
            }
            
            else
            {
                int i=0;
                while(i<g.length()-1)
                {
                    char c1=g.charAt(i),c2=g.charAt(i+1);
                    if(c1==c2&&c1=='0')
                    {
                       g=g.substring(0,i+1)+"1"+g.substring(i+1);
                       i=i+2;
                    }
                    else if(c1==c2&&c2=='1')
                    {
                        g=g.substring(0,i+1)+"0"+g.substring(i+1);
                       i=i+2;
                    }
                    else
                    i++;
                    
                }
                System.out.println(g);
            }
        }
		
	}
}