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 Example {
    static int[] dp;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        //  int t=sc.nextIn
        int t = sc.nextInt();

        while (t > 0) {
            t--;
            String s = sc.next();
            boolean tt = true;
            for (int i = 0; i < s.length() - 1; i++) {
                if (s.charAt(i) != s.charAt(i + 1)) {
                    tt = false;
                    //  System.out.println(s);
                    break;

                }
            }
            if (tt)
                System.out.println(s);
            else {
                StringBuilder ans =new StringBuilder("");
                
                for(int i=1;i<=2*s.length();i++){
                    if(i%2==0)
                        ans.append(1);
                    else
                        ans.append(0);
                }
                System.out.println(ans);
            }

        }


    }

    private static boolean isPrime(int nextInt) {
        for (int i = 2; i * i <= nextInt; i++) {
            if (nextInt % i == 0)
                return false;
        }
        return nextInt != 1;
    }
}