3677 - Count Binary Palindromic Numbers.

Hard

You are given a non-negative integer n.

A non-negative integer is called binary-palindromic if its binary representation (written without leading zeros) reads the same forward and backward.

Return the number of integers k such that 0 <= k <= n and the binary representation of k is a palindrome.

Note: The number 0 is considered binary-palindromic, and its representation is "0".

Example 1:

Input: n = 9

Output: 6

Explanation:

The integers k in the range [0, 9] whose binary representations are palindromes are:

• 0 → "0"

• 1 → "1"

• 3 → "11"

• 5 → "101"

• 7 → "111"

• 9 → "1001"

All other values in [0, 9] have non-palindromic binary forms. Therefore, the count is 6.

Example 2:

Input: n = 0

Output: 1

Explanation:

Since "0" is a palindrome, the count is 1.

Constraints:

• <code>0 <= n <= 10¹⁵</code>