Minimize operations to reduce integer to zero

Q: Minimize operations to reduce integer to zero

This question evaluates algorithmic problem-solving and integer-manipulation skills, specifically assessing the ability to reason about operation counts and binary behavior, and it belongs to the Coding & Algorithms category.

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Question

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You are given a non-negative integer n.

In one operation:

If n is even, you may replace n with n / 2 .
If n is odd, you may replace n with either n + 1 or n - 1 .

Return the minimum number of operations needed to make n = 0.

Input

A single integer n .

Output

An integer: the minimum number of operations to reach 0 .

Constraints

Assume 0 <= n <= 10^9 (or similar large bound).

Examples

n = 0 → 0
n = 7 → 5 (one optimal path: 7→8→4→2→1→0)

Minimize operations to reduce integer to zero

Quick Overview

Input

Output

Constraints

Examples

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