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.

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 $$$121$$$.

Madoka and Math Dad

Examples