A11349. Vlad and a Sum of Sum of Digits

Please note that the time limit for this problem is only 0.5 seconds per test.

Vladislav wrote the integers from $1$ to $n$ , inclusive, on the board. Then he replaced each integer with the sum of its digits.

What is the sum of the numbers on the board now?

For example, if $n=12$ then initially the numbers on the board are: $$$$1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. $$ Then after the replacement, the numbers become: $$ 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3. $$ The sum of these numbers is $1+2+3+4+5+6+7+8+9+1+2+3=51$ . Thus, for $n=12$ the answer is $51$$$.

The first line contains an integer $t$ ( $1 \leq t \leq 10^4$ ) — the number of test cases.

The only line of each test case contains a single integer $n$ ( $1 \leq n \leq 2 \cdot 10^5$ ) — the largest number Vladislav writes.

For each test case, output a single integer — the sum of the numbers at the end of the process.