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:

def inp_n():
    return int(input())

def inp_list():
    return list(map(int, input().split()))

def inp_mul_num():
    return map(int, input().split())

def is_odd(n):
    if n & 1:
        return True
    return False


def is_prime(n):
    i = 2
    while i * i <= n:
        if n%i == 0:
            return False
        i += 1
    return True
from collections import defaultdict
import math


for _ in range(inp_n()):
    l = input()
    n = len(l)
    c = 1
    for i in range(1, n):
        if l[i] == l[i-1]:
            c += 1
    if c == 1:
        print(l)
    elif c == n:
        print(l)
    else:
        s = ''
        f = 0
        for i in range(2*n):
            if f == 0:
                f = 1
                s+='0'
            else:
                f = 0
                s+='1'
        print(s)