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:
import sys
from collections import defaultdict as dd
input=sys.stdin.readline
mod=1000000007
def power(x,y): 
    res = 1
    while (y > 0):  
        if ((y & 1) == 1) : 
            res = (res * x )%m
        y = y >> 1
        x =( x * x )%m
      
    return res%m
for _ in range(int(input())):
    t=input()
    l=[int(t[i]) for i in range(len(t)-1)]
    m="".join([str(i) for i in l])
    c1=l.count(1)
    n=len(l)
    c0=n-c1
    if(c1==0 or c0==0):
        print(m)
    else:
        if(l[0]==0):
            s="0"
            f=0
        else:
            s="1"
            f=1
        
        h=2*n
        for i  in range(1,h-1):
            if(f==0):
                s+=("1")
                f^=1
            else:
                s+=("0")
                f^=1
        print(s)
    
##    x,y=map(int,input().split())
##    a,b=map(int,input().split())
##    print(min((abs(x-y)*a + min(x,y)*b),(x+y)*a))