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: Accepted)

use std::io::Read;

fn calc(a: &Vec<u64>) -> Vec<usize> {
    let n = a.len();
    let m = 15;
    let mut dp = vec![vec![0; n]; m + 1];
    for i in 0..(m + 1) {
        dp[i][n - 1] = 2 * i;
    }
    for i in (0..(n - 1)).rev() {
        let mut x = a[i];
        let mut y = a[i + 1];
        let mut k = 0;
        for j in 0..(m + 1) {
            while x > y {
                k += 1;
                y *= 4;
            }
            if k <= m {
                dp[j][i] = dp[k][i + 1] + 2 * j;
            } else {
                dp[j][i] = dp[m][i + 1] + 2 * j + 2 * (k - m) * (n - 1 - i);
            }
            x *= 4;
        }
    }
    dp[0].clone()
}

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let n: usize = it.next().unwrap().parse().unwrap();
    let mut a: Vec<u64> = (0..n).map(|_| it.next().unwrap().parse().unwrap()).collect();
    let x = calc(&a);
    a.reverse();
    let y = calc(&a);
    let mut ans = x[0];
    for i in 1..n {
        ans = std::cmp::min(ans, x[i] + y[n - i] + i);
    }
    println!("{}", ans);
}

fn main() {
    run();
}