Nine Digits From Three Multiples

Easy

You are given a three-digit number num. Write num, then 2 * num, then 3 * num one after another with no separators, forming a single string of digits. Return True if every digit from 1 to 9 appears in that string exactly once and there is no zero at all. Otherwise return False. For instance, num = 219 produces 219438657, which qualifies.

Example 1

num=273 → True

Gluing 273, 546 and 819 gives 273546819: each digit from 1 to 9 exactly once.

Example 2

num=250 → False

The result is 250500750, which has zeros and repeats.

Example 3

num=111 → False

111222333 uses only three distinct digits.

Constraints

100 ≤ num ≤ 999

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Topics

Hash Table Math

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Input

num=273

Expected

True

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