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 collections import Counter
import itertools
from functools import lru_cache
import sys
import math
###############################################################################
#Helper
def helper():
    pass
###############################################################################
#Solver
def solve():
    s = input()
    count = Counter(list(s))
    if (count['1'] == 0 or count['0'] == 0):
        print(s)
        return
    else:
        ans = ""
        for i in range(len(s)):
            if i == 0:
                ans += s[i]
            else:
                if s[i] == '0' and ans[-1] == '1':
                    ans += s[i]
                elif s[i] == '0' and ans[-1] == '0':
                    ans += '1' + s[i]
                elif s[i] == '1' and ans[-1] == '0':
                    ans += s[i]
                else:
                    ans += '0' + s[i]
        if len(ans) % 2 != 0:
            if ans[-1] == '0':
                ans += '1'
            else:
                ans += '0'
        print(ans)
        return



###############################################################################
#Driver
t = int(input())
for _ in range(t):
    solve()
###############################################################################