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 PYTHON3):

Solution:
def generate(s,l):
	i=0
	while(len(s)<2*l):
		s.append(s[i])
		i+=1
	return s
def subsequence(s1,s):
	j=0
	flag = 1
	for i in range(0,len(s)):
		while j<len(s1) and s1[j]!=s[i]:
			j+=1 
		if j>=len(s1) and s1[j-1]!=s[i]:
			flag=0
	return flag


t=int(input())
for _ in range(0,t):
	s= list(input())
	flag=1
	for i in range(len(s)-1):
		if s[i]!=s[i+1]:
			flag=0
			break
	if flag:
		print("".join(s))
	else:
		for k in range(2,len(s)+1):
			s1 = ['1','0']
			s2 = ['0','1']
			s1 = generate(s1,len(s))
			s2 = generate(s2,len(s))
			if subsequence(s1,s):
				print("".join(s1))
				break
			elif subsequence(s2,s):
				print("".join(s1))
				break