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 sys import stdin

def main():
    tests_num = int(stdin.readline())
    tests = []
    for t in range(tests_num):
        received = stdin.readline()
        string = received[0:len(received)-1:]
        tests.append(string)

    for test in tests:

        if len(test) == 2 or len(test) == 1:
            print(test)
            continue

        chars = {}
        for char in test:
            if char in chars:
                continue
            else:
                chars[char] = True

        if len(chars) == 1:
            print(test)
            continue
        
        res = ""
        pos = 0

        for char in test[:-1:]:
            if char == "1" and test[pos + 1] == "1":
                res += "10"
            elif char == "0" and test[pos +1] == "0":
                res += "01"
            else:
                res += char
            pos += 1

        res += test[-1]

        print(res)

main()