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.lang.*;
import java.text.*;
import java.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int t = scanner.nextInt();
		while (t-- > 0)
		{
			String st = scanner.next();
			int size = st.length();
			int[] ss = new int[2 * size];
			int flag = 1;
			int j = 0;
			char[] a = new char[2];
			a[0] = 'a';
			a[1] = 'a';
			for (int i = 0; i < size; ++i)
			{
				if (st.charAt(i) == '1')
					a[1] = 1;
				else if (st.charAt(i) == '0')
					a[0] = 0;
			}
			if (a[0] == 'a' || a[1] == 'a')
			{
				System.out.println(st);
				continue;
			}
			
			for (int i = 0; i < size; ++j)
			{
				if (flag == 1)
				{
					ss[j] = 1;
					if (st.charAt(i) == '1')
						++i;
				}
				else if (flag == -1)
				{
					ss[j] = 0;
					if (st.charAt(i) == '0')
						++i;
				}
				flag *= -1;
			}
			int check = -1;
			for (int i = 0; i < j; ++i)
			{
				check = ss[i];
				System.out.print(ss[i]);
			}
			if (check == 1)
				System.out.print("0");
			System.out.print("\n");
		}
		scanner.close();
	} // end main
} // end class