Background

Description

We'll say that a positive int divides itself if every digit in the number divides into the number evenly. So for example 128 divides itself since 1, 2, and 8 all divide into 128 evenly. We'll say that 0 does not divide into anything evenly, so no number with a 0 digit divides itself. Note: use % to get the rightmost digit, and / to discard the rightmost digit.

Format

Input

Output

Samples

128

true

12

true

120

false

Limitation

1s, 1024KiB for each test case.