Problem Description

bj12z_jiasiyuan wants you to output three-digit numbers that meet the following conditions, where the hundreds place is $a$, the tens place is $b$, and the units place is $c$.

• $a$ is a digit between $1$ and $9$, $b$ is a digit between $0$ and $9$, and $c$ is a digit between $0$ and $9$.
• $a \times 10 + b$ is a multiple of $k$, and $b \times 10 + c$ is a multiple of $k$.
• $a \times 100 + b \times 10 + c$ is a multiple of $k$.

You need to output all three-digit numbers that satisfy these conditions in ascending order, one per line.

If there are no three-digit numbers that meet the requirements, output a single line None!.

Input Format

Input consists of a single integer $k$.

Output Format

Output all three-digit numbers that meet the conditions in ascending order, one per line.

If there are no three-digit numbers that meet the requirements, output a single line None!.

Sample Input and Output

Sample Input #1

8

Sample Output #1

240
248
400
408
480
488
640
648
800
808
880
888

Sample Input #2

19

Sample Output #2

None!

Notes

Data Range and Constraints

• For $50\%$ of the test cases, $1 \leq k \leq 10$.
• For $100\%$ of the test cases, $1 \leq k \leq 20$.

见题面 Input 部分

见题面 Output 部分