A14932. Madoka and Math Dad

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!

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.

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

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 $121$ .