Problem Description

Let $a_1, a_2, \cdots$ be an integer sequence beginning with $a_1 = 1$. For $n \ge 1$, $a_{n+1}$ is the sum of $a_n$ and the sum of digits of $a_n$. That’s why we name the sequence a new Self-describing sequence.

The sequence starts with $1, 2, 4, 8, 16, 23, 28, 38, 49, \cdots$ and we also define the prefix sum $s_n = a_1 + a_2 + \cdots + a_n$. For given positive integer $n$, find $a_n$ and $s_n$.

Input Format

The first line of input consists an integer $T$ ($T \le 32768$), indicating the total number of test cases. Each of the following $T$ lines provides an integer $n$ ($n \le 10^{17}$).

Output Format

For each test case output its case label first. Then for given $n$, output $a_n$ and $s_n$. Since the prefix sum is large, you only need to output $s_n \bmod 1000000009$. However you should output $a_n$ as its exact value.

7
6
66
666
6666
66666
123456789
31415926535897932

Case #1: 23 54
Case #2: 752 20862
Case #3: 10949 3407733
Case #4: 136193 441127485
Case #5: 1698899 717710112
Case #6: 5061289531 990040993
Case #7: 2508156610654066874 660828136