use vstd::prelude::*;

fn main() {}

verus! {

pub struct Solution;

impl Solution {
    pub open spec fn spec_steps(n: int) -> int
        decreases n
    {
        if n <= 0 {
            0
        } else if n % 2 == 0 {
            1 + Self::spec_steps(n / 2)
        } else {
            1 + Self::spec_steps(n - 1)
        }
    }

    pub fn number_of_steps(num: i32) -> (result: i32)
        requires
            0 <= num <= 1_000_000,
        ensures
            result == Self::spec_steps(num as int),
    {
        let mut n = num;
        let mut steps = 0i32;
        while n > 0 {
            if n % 2 == 0 {
                n = n / 2;
            } else {
                n = n - 1;
            }
            steps = steps + 1;
        }
        steps
    }
}

}