C. Vlad and a Sum of Sum of Digits
time limit per test
0.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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$$$.

Input

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.

Output

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

Example
Input
7
12
1
2
3
1434
2024
200000
Output
51
1
3
6
18465
28170
4600002