Total Hamming Weight Sum

Given a non-negative integer \( n \), your task is to compute the total number of '1' bits (also known as the Hamming weight) in the binary representations of all integers from \( 0 \) to \( n \) inclusive.

For example, if \( n = 5 \), the binary representations are:

• 0: 0 (0 ones)
• 1: 1 (1 one)
• 2: 10 (1 one)
• 3: 11 (2 ones)
• 4: 100 (1 one)
• 5: 101 (2 ones)

Thus, the total number of ones is \(0+1+1+2+1+2=7\). Please note that if \( n = 0 \), the output should be \( 0 \).

inputFormat

The input contains a single non-negative integer \( n \) provided through standard input. \( n \) satisfies \( 0 \leq n \leq 10^9 \).

outputFormat

Output a single integer which is the total count of '1' bits in the binary representations of all integers from \( 0 \) to \( n \) inclusive.

5

7