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,stdout
import bisect
import math
import itertools

#Testing bulild system for python, handling inputs in sublime
#Hope it works

_INPUT=-1
input=[]
def I():
    global _INPUT
    _INPUT += 1
    INPUT = list(map(int,input[_INPUT].split()))
    if len(INPUT) == 1:
        return INPUT[0]
    else:
        return INPUT   

def IS():
    global _INPUT
    _INPUT += 1
    INPUT = list(map(str,input[_INPUT].split()))
    if len(INPUT) == 1:
        return INPUT[0]
    else:
        return INPUT 
       
def IA():
    global _INPUT
    _INPUT += 1
    INPUT = list(map(int,input[_INPUT].split()))
    return INPUT    

def IAS():
    global _INPUT
    _INPUT += 1
    INPUT = list(map(str,input[_INPUT].split()))
    return INPUT

#stdin = open("input.txt","r")
ONLINE_JUDGE = not __debug__
if ONLINE_JUDGE:
    stdin = open("input.txt", "r")

input = stdin.readlines()

if __name__=="__main__":

    t = I()
    for _ in range(t):
        s=IS()
        st = set()
        ans = ""
        for i in range(len(s)-1):
            st.add(s[i])
            ans += s[i]
            if s[i]==s[i+1]:
                ans += str(ord('1')-ord(s[i]))
        st.add(s[len(s)-1])
        ans += s[len(s)-1]
        if len(st)==1:
            ans=s
        print(ans)