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 PYTHON):

Solution:
from sys import stdin, stdout  
  
def main(): 
	N = int(stdin.readline().rstrip()) 
	for x in range(N):
		t = stdin.readline().rstrip()
		ans = t[0]
		aux = ['1','0']
		if t.find('0') >= 0 and  t.find('1') >= 0:
			for i in range(0, len(t) - 1):
				if t[i+1] == t[i]:
					ans+= aux[int(t[i+1])] + t[i+1]
				else:
					ans+=t[i+1]
			if len(ans) % 2 != 0:
				ans+=aux[int(ans[len(ans) - 1])]
			stdout.write(str(ans)+'\n')
		else:
			stdout.write(str(t*2)+'\n')
if __name__ == "__main__": 
	main()