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:
#add 0/1s anywhere in s to reduce the period
t=int(input())
while(t):
    s=input()
    if('0' in s and '1' not in s):
        print(s)
    elif('0' not in s and '1' in s):
        print(s)
    elif('0'in s and '1' in s):
        k=0
        j=len(s)
        i=1
        while(i<j+k):
            if(s[i-1]=='0' and s[i]=='0'):
                s=s[:i]+'1'+s[i:]
                k+=1
                #print('no')
                
            elif(s[i-1]=='1' and s[i]=='1'):
                s=s[:i]+'0'+s[i:]
                #print('oh')
                k+=1
            #print("i is ",i," len is ",len(s))
            i+=1
        print(s)
    t-=1