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:
import sys

def main():
    t = int(sys.stdin.readline())
    strings = []
    for i in range(t):
        strings.append(list(sys.stdin.readline().strip()))
    sols = []
    for i in range(t):
        ones = set()
        zeroes = set()
        if strings[i].count(strings[i][0]) == len(strings[i]):
            sols.append("".join(strings[i]))
        else:
            for j in range(1, len(strings[i])):
                if strings[i][j] == '0' and strings[i][j-1] == '0':
                    ones.add(j)
                elif strings[i][j] == '1' and strings[i][j-1] == '1':
                    zeroes.add(j)
        
            fixed = ""
            for j in range(0, len(strings[i])):
                if j in ones:
                    fixed += "10"
                elif j in zeroes:
                    fixed += "01"
                else:
                    fixed += strings[i][j]
            sols.append(fixed)

    for i in sols:
        sys.stdout.write(i + "\n")




if __name__ == "__main__":
    main()