Self-Dividing Number

Background

In the world of numbers, some possess unique properties. Today, we will explore a special type of number: the "self-dividing number."

Problem Description

We define a positive integer as a "self-dividing number" if every digit in the number divides into the number evenly. For example, 128 is a self-dividing number because 1, 2, and 8 all divide into 128 evenly. If a number contains the digit 0, it is not a self-dividing number, as 0 cannot divide anything evenly.

Hint: Use the modulo operator (%) to get the rightmost digit, and the integer division operator (/) to discard the rightmost digit.

Input Format

Input is given from standard input in the following format.

A positive integer $N$.

Output Format

Output is printed to standard output in the following format.

Output true if $N$ is a self-dividing number; otherwise, output false.

Sample

128

true

12

true

120

false

Sample Explanation

Sample 1: For the number 128:

• 1 divides 128 ($128 \div 1 = 128$)
• 2 divides 128 ($128 \div 2 = 64$)
• 8 divides 128 ($128 \div 8 = 16$) All digits divide 128, so 128 is a self-dividing number.

Sample 2: For the number 12:

• 1 divides 12 ($12 \div 1 = 12$)
• 2 divides 12 ($12 \div 2 = 6$) All digits divide 12, so 12 is a self-dividing number.

Sample 3: For the number 120:

• It contains the digit 0. According to the rule, it is not a self-dividing number.

Constraints

The time limit for each test case is 1 second, and the memory limit is 1024 KiB.