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;
int main() {
  long long int test;
  cin >> test;
  while (test--) {
    string s1;
    cin >> s1;
    long long int n1 = s1.size();
    if (n1 == 1 || n1 == 2)
      cout << s1 << endl;
    else {
      int z = 0, o = 0;
      for (long long int i = 0; i < n1; i++) {
        if (s1[i] == '1')
          o++;
        else
          z++;
      }
      if (z == 0 || o == 0)
        cout << s1 << endl;
      else {
        string s;
        if (s1[0] == '1') {
          long long int i = 1;
          s.push_back(s1[0]);
          int pt = 1;
          while (i != n1) {
            if (pt % 2 != 0) {
              if (s1[i] == '0') {
                s.push_back(s1[i]);
                i++;
                pt++;
                continue;
              } else {
                s.push_back('0');
                pt++;
                continue;
              }
            } else {
              if (s1[i] == '1') {
                s.push_back(s1[i]);
                i++;
                pt++;
                continue;
              } else {
                s.push_back('1');
                pt++;
                continue;
              }
            }
          }
        } else {
          long long int i = 1;
          s.push_back(s1[0]);
          int pt = 1;
          while (i != n1) {
            if (pt % 2 != 0) {
              if (s1[i] == '1') {
                s.push_back(s1[i]);
                i++;
                pt++;
                continue;
              } else {
                s.push_back('1');
                pt++;
                continue;
              }
            } else {
              if (s1[i] == '0') {
                s.push_back(s1[i]);
                i++;
                pt++;
                continue;
              } else {
                s.push_back('0');
                pt++;
                continue;
              }
            }
          }
        }
        cout << s << endl;
      }
    }
  }
  return 0;
}