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.io.BufferedReader;
import java.io.InputStreamReader;

public class Ques1 {
    public static void main(String[] args) throws Exception {
        BufferedReader z = new BufferedReader(new InputStreamReader(System.in));
        int t=Integer.parseInt(z.readLine());
        while(t-->0){
            String s = z.readLine();
            int n=s.length(), i, j=0;
            if(n<=2 || !s.contains("0") || !s.contains("1")){
                System.out.println(s);
                continue;
            }
            StringBuilder m = new StringBuilder();
            for(i=0;i<n;i++){
                m.append('1');
                m.append('0');
            }
            for(i=0;i<2*n && j<n;i++){
                if(m.charAt(i)==s.charAt(j)){
                    j++;
                }
            }
            if (j != n) {
                m.deleteCharAt(0);
                m.append('1');
            }
            System.out.println(m);
        }
    }
}