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 tc in range(T):
    t = input()
    
    if "1" in t and "0" in t:
        #res= ""
        if t[0] == "0":
            i = 0
            c1 = 0
            uc1 = 0
            count0 = 0
            while(i<len(t)):
                if t[i] == 0:
                    count0 += 1
                    uc1 += max(0, c1 - 1)
                    c1 = 0
                    i+=1
                else:
                    c1 += 1
                    i+=1
            uc1 += max(0, c1-1)
            
            netcount = count0 + uc1
            s = "01" * netcount
        else:
            i = 0
            c0 = 0
            uc0 = 0
            count1 = 0
            while(i<len(t)):
                if t[i] == 1:
                    count1 += 1
                    uc0 += max(0, c0 - 1)
                    c0 = 0
                    i+=1
                else:
                    c0 += 1
                    i+=1
            uc0 += max(0, c0-1)
            
            netcount = count1 + uc0
            s = "10" * netcount
      
        
    else:
        s = t
    print(s)