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:
from math import gcd
from sys import stdin
inp = stdin.readline

t = int(inp().strip())

for _ in range(t):
    x = [int(x) for x in str(inp().strip())]
    if min(x) == max(x):
        print(''.join(map(str,x)))
    else:
        ans = []
        if x.count(0) == x.count(1):
            for i in range(len(x)*2):
                ans.append(i%2)
            if x[0] == 1:
                ans.reverse()
            print(''.join(map(str,ans)))
        else:
            maxCount = max(x.count(0), x.count(1))
            for i in range(len(x)*2):
                ans.append(i % 2)
            if x[0] == 1:
                ans.reverse()
            print(''.join(map(str,ans)))