Problem:
Score : 800 points

Problem Statement

There are N positive integers A_1, A_2, ..., A_N.
Takahashi can perform the following operation on these integers any number of times:

Choose 1 \leq i \leq N and multiply the value of A_i by -2.

Notice that he multiplies it by minus two.

He would like to make A_1 \leq A_2 \leq ... \leq A_N holds.
Find the minimum number of operations required. If it is impossible, print -1.

Constraints

1 \leq N \leq 200000

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the answer.

Sample Input 1

4
3 1 4 1

Sample Output 1

3

One possible solution is:

Choose i=4 and multiply the value of A_4 by -2. A_1, A_2, A_3, A_4 are now 3, 1, 4, -2.

Choose i=1 and multiply the value of A_1 by -2. A_1, A_2, A_3, A_4 are now -6, 1, 4, -2.

Choose i=4 and multiply the value of A_4 by -2. A_1, A_2, A_3, A_4 are now -6, 1, 4, 4.

Sample Input 2

5
1 2 3 4 5

Sample Output 2

0

A_1 \leq A_2 \leq ... \leq A_N holds before any operation is performed.

Sample Input 3

8
657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097

Sample Output 3

7

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

use std::collections::HashMap;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

fn count(a: &[f64]) -> i64 {
    let mut last_num = a[0];
    let mut count: i64 = 0;
    for i in 1..a.len() {
        let mut num = a[i];
        if num < last_num {
            let mut temp_inc = (last_num - num).ceil() as i64;
            if temp_inc % 2 == 1 {
                temp_inc += 1;
            }
            count += temp_inc;
            num += temp_inc as f64;
        }
        last_num = num;
    }
    count
}

fn main() {
    let _: usize = read();
    let a = read_vec::<i64>();
    let a = a.iter().map(|x| (*x as f64).log2()).collect::<Vec<_>>();
    // println!("{:?}", a);
    let split_idx = 1;
    let (a1, a2) = a.split_at(split_idx);
    let mut ans = count(&a1) + count(&a2);
    if split_idx > 0 && a[split_idx] < a[split_idx - 1] {
        ans += split_idx as i64;
    }
    println!("{:?}", ans);
}