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:
# -*- coding: utf-8 -*-
"""
Created on Mon Jun 15 13:22:05 2020

@author: Mridul Garg
"""

q = int(input())
for _ in range(q):
#    x, y = list(map(int, input().split(" ")))
#    a, b = list(map(int, input().split(" ")))
    s = input()
    n = len(s)
    if n <= 2:
        print(s)
        continue
    
    o, t = 0, 0
    for i in s:
        if i == "1":
            o += 1
        else:
            t += 1
    if t*o == 0:
        print(s)
        continue
    
    a = ""
    i = 0
    while i < n-1:
        if s[i] == s[i+1]:
            a += s[i]
            if s[i] == "1":
                a += "0"
            else:
                a += "1"
            i += 1
        
        else:
            a += s[i]
#            a += s[i+1]
            i += 1
    a += s[-1]
    
        
    print(a)            
#        else:
#            s1 = -1*MAX*b + (MAX-MIN)*a
#            s2 = a*abs(x) + a*abs(y)
#        
#            print(min(s1, s2))
#