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.util.regex.Matcher;
import java.util.regex.Pattern;
import java.io.*;
 
 
public final class Solution {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int t=sc.nextInt();
		while(t-->0) {
			String s=sc.next();
			int l1=0, l2=0;
			for(int i=0;i<s.length();i++) {
				if(s.charAt(i)=='1') l1++;
				else l2++;
			}
			int size = 2*(l1+l2); 
			if(l1==0 || l2==0)
				size = Math.max(l1, l2);
			
			int[] a=new int[size];
			for(int i=0;i<a.length;i++) {
				if(l1==0) a[i]=0;
				else if(l2==0) a[i]=1;
				else if(s.charAt(0)=='1') {
					if(i%2==0) a[i]=1;
					else a[i]=0;
				}else {
					if(i%2==0) a[i]=0;
					else a[i]=1;
				}
			}
			for(int i=0;i<a.length;i++) System.out.print(a[i]);
			
			System.out.println();
				
		}
	}
}