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 allSame(li):
    c = li[0] 
    for i in li:
        if(i!=c):
            return False 
    return True

for _ in range(int(input())):
    s = input() 
    li = list(s)

    if(allSame(li)):
        for i in li:
            print(i , end = '') 
        print()
        continue

    #print(li) 
    i = 1
    print(li[0] , end = "") 
    #we will make a string of type 01010101..... 
    ctr = 1 
    while(i<len(s)):
        if(li[i] == li[i-1]):
            if(li[i] == '1'):
                print('0' , end = '') 
            else:
                print('1' , end = '') 
            ctr += 1 
        print(li[i],end='')
        ctr += 1
        i += 1

    if(ctr%2 == 1):
        if(li[0] == '0'):
            print('1' , end = '')
        else:
            print('0' , end = '')

    print()