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B. Binary Period
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$2 \cdot |t|$$$;
  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 $$$T$$$ ($$$1 \le T \le 100$$$) — the number of test cases.

Next $$$T$$$ lines contain test cases — one per line. Each line contains string $$$t$$$ ($$$1 \le |t| \le 100$$$) 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 $$$1$$$.