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 T;
char s[205], t[205];
int main() {
  scanf("%d", &T);
  while (T--) {
    scanf("%s", t + 1);
    int len = strlen(t + 1), flag = 1;
    for (int i = 2; i <= len; ++i)
      if (t[i] != t[1]) flag = false;
    if (flag) {
      printf("%s\n", t + 1);
      continue;
    }
    int cur = 0;
    for (int i = 1; i <= len; ++i) {
      s[++cur] = t[i];
      if (s[cur] == s[cur - 1]) {
        s[cur] = '0' + (s[cur] - '0' ^ 1);
        --i;
      }
    }
    s[cur + 1] = 0;
    printf("%s\n", s + 1);
  }
  return 0;
}