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 solve(s):
	period1 = True
	period2 = True
	ans = []
	for i in range(len(s) - 1):
		if s[i] != s[i + 1]:
			period1 = False
			break
	for i in range(len(s) - 2):
		if s[i] != s[i + 2]:
			period2 = False
			break
	if period1 or period2:
		return s
	s = [c for c in s]
	i = 0
	length = len(s)
	while i < length - 1:
		if s[i] == s[i + 1]:
			s.insert(i + 1, str(1 - int(s[i])))
			length += 1
		i += 1
			# s.append(s[i])

		# print(s)
	return "".join(s)


for _ in range(int(input())):
	s = input()
	print(solve(s))