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)

macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut iter = $ s . split_whitespace ( ) ; input_inner ! { iter , $ ( $ r ) * } } ; ( iter = $ iter : ident , $ ( $ r : tt ) * ) => { let s = { use std :: io :: Read ; let mut s = String :: new ( ) ; std :: io :: stdin ( ) . read_to_string ( & mut s ) . unwrap ( ) ; s } ; let mut $ iter = s . split_whitespace ( ) ; input_inner ! { $ iter , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { let s = { use std :: io :: Read ; let mut s = String :: new ( ) ; std :: io :: stdin ( ) . read_to_string ( & mut s ) . unwrap ( ) ; s } ; let mut iter = s . split_whitespace ( ) ; input_inner ! { iter , $ ( $ r ) * } } ; }
macro_rules ! input_inner { ( $ iter : expr ) => { } ; ( $ iter : expr , ) => { } ; ( $ iter : expr , mut $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let mut $ var = read_value ! ( $ iter , $ t ) ; input_inner ! { $ iter $ ( $ r ) * } } ; ( $ iter : expr , mut $ var : ident $ ( $ r : tt ) * ) => { input_inner ! { $ iter , mut $ var : usize $ ( $ r ) * } } ; ( $ iter : expr , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ iter , $ t ) ; input_inner ! { $ iter $ ( $ r ) * } } ; ( $ iter : expr , $ var : ident $ ( $ r : tt ) * ) => { input_inner ! { $ iter , $ var : usize $ ( $ r ) * } } ; }
macro_rules ! read_value { ( $ iter : expr , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ iter , $ t ) ) ,* ) } ; ( $ iter : expr , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ iter , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ iter : expr , { chars : $ base : expr } ) => { read_value ! ( $ iter , String ) . chars ( ) . map ( | c | ( c as u8 - $ base as u8 ) as usize ) . collect ::< Vec < usize >> ( ) } ; ( $ iter : expr , { char : $ base : expr } ) => { read_value ! ( $ iter , { chars : $ base } ) [ 0 ] } ; ( $ iter : expr , chars ) => { read_value ! ( $ iter , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ iter : expr , char ) => { read_value ! ( $ iter , chars ) [ 0 ] } ; ( $ iter : expr , usize1 ) => { read_value ! ( $ iter , usize ) - 1 } ; ( $ iter : expr , $ t : ty ) => { $ iter . next ( ) . unwrap ( ) . parse ::<$ t > ( ) . unwrap ( ) } ; }
fn count1(x: usize, y: usize, base: usize) -> usize {
    let mut cnt = 0;
    let mut x = x;
    while x * base <= y {
        x *= base;
        cnt += 1;
    }
    cnt
}
fn count2(y: usize, x: usize, base: usize) -> usize {
    let mut cnt = 0;
    let mut x = x;
    while x < y {
        x *= base;
        cnt += 1;
    }
    cnt
}
fn main() {
    input! { n, a: [usize; n] };
    let mut b = vec![0; n + 1];
    let mut c = vec![0; n + 1];
    let mut stack = vec![(0i64, 1)];
    for i in (0..n - 1).rev() {
        b[i] = b[i + 1];
        let k = count1(a[i], a[i + 1], 4) as i64;
        let m = stack.last().unwrap().0;
        if k > 0 {
            stack.push((m - k, 1));
        } else {
            let l = count2(a[i], a[i + 1], 4) as i64;
            let mut t = (m + l, 1);
            while let Some(u) = stack.pop() {
                if u.0 > t.0 {
                    stack.push(u);
                    break;
                } else {
                    t.1 += u.1;
                    b[i] += (t.0 - u.0) * u.1 * 2;
                }
            }
            stack.push(t);
        }
    }
    let mut stack = vec![(0i64, 1)];
    for i in 0..n - 1 {
        c[i + 2] = c[i + 1];
        let k = count1(a[i + 1], a[i], 4) as i64;
        let m = stack.last().unwrap().0;
        if k > 0 {
            stack.push((m - k, 1));
        } else {
            let l = count2(a[i + 1], a[i], 4) as i64;
            let mut t = (m + l, 1);
            while let Some(u) = stack.pop() {
                if u.0 > t.0 {
                    stack.push(u);
                    break;
                } else {
                    t.1 += u.1;
                    c[i + 2] += (t.0 - u.0) * u.1 * 2;
                }
            }
            stack.push(t);
        }
    }
    let mut ans = 1_000_000_000_000_000_000;
    for i in 0..n + 1 {
        ans = std::cmp::min(ans, b[i] + c[i] + i as i64);
    }
    println!("{}", ans);
}