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>
#pragma GCC optimize(2)
#pragma G++ optimize(2)
using namespace std;
const int N = 1E5 + 10;
int main() {
  string str;
  int t;
  int cnt[2];
  scanf("%d", &t);
  while (t--) {
    cin >> str;
    memset(cnt, 0, sizeof cnt);
    for (register int i = 1; i <= str.size(); ++i) {
      if (str[i - 1] == '0')
        cnt[0]++;
      else
        cnt[1]++;
    }
    if (cnt[0] == 0 || cnt[1] == 0) {
      cout << str << endl;
    } else {
      printf("%c", str[0]);
      for (register int i = 2; i <= str.size(); ++i) {
        if (str[i - 2] == str[i - 1]) {
          if (str[i - 2] == '0')
            printf("1");
          else
            printf("0");
        }
        printf("%c", str[i - 1]);
      }
      printf("\n");
    }
  }
  return 0;
}