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:
t = int(input())

for _ in range(t):
    
    s = input()
    n = len(s)
    
    if n==1 or n==2:
        print(s)
        continue
        
    zeros = s.count('0')
    ones = s.count('1')
    
    d = max(zeros, ones)
    ans =''
    if(zeros>0 and ones>0):
        if(s[0]=='0'):
            j = 0
            while j<n-1:
                if s[j]=='0' and s[j+1]!='1':
                    ans += '01'
                elif s[j]=='0' and s[j+1]=='1':
                    ans += '01'
                    j+=1
                elif s[j]=='1' and s[j-1]!='0':
                    ans += '01'
                
                j+=1
            if(s[n-1]=='0'):
                ans+='01'
            elif(s[n-1]=='1' and s[n-2]!='0'):
                ans += '01'
        else:
            j = 0
            while j<n-1:
                if s[j]=='1' and s[j+1]!='0':
                    ans += '10'
                elif s[j]=='1' and s[j+1]=='0':
                    ans += '10'
                    j+=1
                elif s[j]=='0' and s[j-1]!='1':
                    ans += '10'
                j+=1
            if(s[n-1]=='1'):
                ans+='10'
            elif(s[n-1]=='0' and s[n-2]!='1'):
                ans += '10'
    else:
        ans = s
        
    print(ans)