Solve the programming task below in a Python markdown code block.
Madoka finally found the administrator password for her computer. Her father is a well-known popularizer of mathematics, so the password is the answer to the following problem.

Find the maximum decimal number without zeroes and with no equal digits in a row, such that the sum of its digits is $n$.

Madoka is too tired of math to solve it herself, so help her to solve this problem!


-----Input-----

Each test contains multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 1000$) — the number of test cases. Description of the test cases follows.

The only line of each test case contains an integer $n$ ($1 \le n \le 1000$) — the required sum of the digits.


-----Output-----

For each test case print the maximum number you can obtain.


-----Examples-----

Input
5
1
2
3
4
5
Output
1
2
21
121
212


-----Note-----

The only numbers with the sum of digits equal to $2$ without zeros are $2$ and $11$. But the last one has two ones in a row, so it's not valid. That's why the answer is $2$.

The only numbers with the sum of digits equal to $3$ without zeros are $111$, $12$, $21$, and $3$. The first one has $2$ ones in a row, so it's not valid. So the maximum valid number is $21$.

The only numbers with the sum of digits equals to $4$ without zeros are $1111$, $211$, $121$, $112$, $13$, $31$, $22$, and $4$. Numbers $1111$, $211$, $112$, $22$ aren't valid, because they have some identical digits in a row. So the maximum valid number is $121$.