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:
# Contest No.: Edu 86
# Problem No.: B
# Solver:      JEMINI
# Date:        20200426

import sys

def main():
    t = int(input())
    for _ in range(t):
        word = sys.stdin.readline().strip()
        cnt = 0
        for i in word:
            if i == "0":
                cnt -= 1
            else:
                cnt += 1
        if abs(cnt) == len(word):
            print(word)
        else:
            ans = word[0]
            i = 0
            while i < len(word):
                if word[i] == "1":
                    if ans[-1] == "0":
                        ans += "1"
                        i += 1
                    else:
                        ans += "01"
                        i += 1
                else:
                    if ans[-1] == "1":
                        ans += "0"
                        i += 1
                    else:
                        ans += "10"
                        i += 1
            print(ans)

    return

if __name__ == "__main__":
    main()