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:
for lo in range(int(input())):
    st = input()
    l = len(st)
    p = st[0]
    ans = p
    c = 0
    for i in range(1,l):
        if st[i]!=st[i-1]:
            c = 1
            break
    if c==0:
        print(st)
        continue
    for i in range(1,l):
        if st[i]==p:
            if p=='0':
                ans+='1'
            else:
                ans+='0'
            ans+=st[i]
        else:
            p = st[i]
            ans+=st[i]
    c1 = 0
    c2 = 0
    for i in ans:
        if i=='0':
            c1+=1
        else:
            c2+=1
    if c1!=c2:
        if c1>c2:
            ans+='1'
        else:
            ans+='0'
    print(ans)