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.*;
import java.lang.*;
import java.io.*;
public class Main
{   
    static Scanner sc = new Scanner(System.in);
    static PrintWriter out = new PrintWriter(System.out);
    
    public static void main(String args[]) throws Exception
    {
        int t=Integer.parseInt(sc.next());
        while(t-->0){
            String str=sc.next();
            if(str.length()<=2){
                out.println(str);
            }
            else{
                boolean flag=true;
                for(int i=1;i<str.length();i++){
                    if(str.charAt(i)!=str.charAt(i-1)){
                        flag=false;
                        break;
                    }
                }
                if(flag){
                    out.println(str);
                }
                else{
                    String ans=""+str.charAt(0);
                    for(int i=1;i<str.length();i++){
                        if(str.charAt(i)!=str.charAt(i-1)){
                            ans+=str.charAt(i);
                        }
                        else{
                            if(str.charAt(i)=='1') ans+='0';
                            else ans+='1';
                            ans+=str.charAt(i);
                        }
                    }
                    out.println(ans);
                }
            }
        }
        out.close();
    }
}