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 Main {
    public static void main(String[] args) {
        Scanner console = new Scanner(System.in);
        int n = console.nextInt();
        for (int i = 0; i < n; i++) {
            bin(console.next());
        }
    }
    public static void bin(String digits) {
        if (!digits.contains("0") || !digits.contains("1")) {
            System.out.println(digits);
            return;
        }
        boolean check = true;
        for (int i = 0; i < digits.length()-2; i++) {
            if (!digits.substring(i, i+2).equals("10") || !digits.substring(i, i+2).equals("01")) {
                check = false;
            }
        }
        if (check) {
            System.out.println(digits);
            return;
        }
        int zero = 0;
        int one = 0;
        for (int i = 0; i < digits.length(); i++) {
            if (digits.substring(i, i+1).equals("1")) {
                one++;
            } else {
                zero++;
            }
        }
        String newDigits = "";
        if (digits.substring(0, 1).equals("1")) {
            newDigits = "10";
            newDigits = newDigits.repeat(digits.length());
        } else {
            newDigits = "01";
            newDigits = newDigits.repeat(digits.length());
        }
        if (newDigits.length() <= 2 * digits.length()) {
            System.out.println(newDigits);
        } else {
            System.out.println(digits);
        }
    }
}