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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
void solveTest() {
  string tt;
  cin >> tt;
  int n = tt.length();
  tt = "#" + tt;
  bool isOne = true;
  for (int i = 1; i <= n; i++)
    if (tt[i] != tt[1]) isOne = false;
  if (isOne) {
    for (char c : tt)
      if (c != '#') cout << c << "";
    cout << "\n";
    return;
  }
  string ans = "";
  ans.push_back(tt[1]);
  for (int i = 2; i <= n; i++) {
    if (tt[i] == ans.back()) {
      if (tt[i] == '1')
        ans.push_back('0');
      else
        ans.push_back('1');
    }
    ans.push_back(tt[i]);
  }
  cout << ans << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int tt;
  cin >> tt;
  while (tt--) solveTest();
  return 0;
}