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:
import java.util.*;
public class test

{
    public static void main(String[]args)
    {
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        sc.nextLine();
        
        for(int l=1;l<=t;l++){
        String str=sc.nextLine();
        
        char c=str.charAt(0);
        boolean flag=true;
        for(int i=0;i<str.length();i++)
        {
            if(str.charAt(i)!=c)
            {
                flag=false;break;
            }
        }
        if(flag==true)
        System.out.print(str);
        else
        {
            for(int i=0;i<str.length();i++)
        {
            if(i==0)
            {
                System.out.print(str.charAt(i));
            }
            else
            {
                c=str.charAt(i-1);
                if(c==str.charAt(i))
                {
                    if(c=='1')
                    System.out.print(0+""+1);
                    else
                    System.out.print(1+""+0);
                }
                else
                {
                    System.out.print(str.charAt(i));
                }
            }
        }
        }
        System.out.println();
        }
    }
}