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 scan = new Scanner(System.in);
        resolve(scan);
        scan.close();
    }

    final private static void resolve(Scanner scan) {
        int t = scan.nextInt();
        while (t-- != 0) {
            String str = scan.next();
            boolean hasOne = false, hasZero = false;
            for (char ch : str.toCharArray()) {
                if (ch == '0') {
                    hasZero = true;
                } else {
                    hasOne = true;
                }
            }
            if (hasZero && hasOne) {
                boolean preOne = false, preZero = false;
                ArrayList<Character> all = new ArrayList<Character>();
                for (char ch : str.toCharArray()) {
                    if (preOne && ch == '1') {
                        all.add('0');
                    } else if (preZero && ch == '0') {
                        all.add('1');
                    }
                    if (ch == '0') {
                        preOne = false;
                        preZero = true;
                    } else {
                        preOne = true;
                        preZero = false;
                    }
                    all.add(ch);
                }
                all.add('\n');
                for (char ch : all) {
                    System.out.print(ch);
                }
            } else {
                System.out.println(str);
            }
        }
    }
}