Shuffle the Digits Into a Power of Two

Medium

You are given a positive integer number. You may rearrange its digits in any order (including leaving them as they are), as long as the first digit is not zero. Return True if some such rearrangement is a power of two (1, 2, 4, 8, 16, …), and False otherwise.

Example 1

number=821 → True

The digits 8, 2, 1 can form 128 = 2⁷.

Example 2

number=23 → True

Only 23 and 32 are possible, and 32 = 2⁵ works.

Example 3

number=40 → False

Zero cannot go first, so only 40 remains, and it is not a power of two.

Constraints

1 ≤ number ≤ 10⁹

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Topics

Hash Table Math Counting Enumeration Sorting

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Input

number=821

Expected

True

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