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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

//#define TEST
using System;
using System.Collections.Generic;
using System.Linq;
class Program{
    static void Main(){
        int n = int.Parse(Console.ReadLine());
        long[] a = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long min = long.MaxValue;
        for (int i = 0;i < n;i++)
            min = Math.Min(min,a[i]);
#if TEST
        Console.WriteLine("min : {0}",min);
#endif
        List<int> min_index = new List<int>();
        for (int i = 0;i < n;i++)
            if (a[i] == min)
                min_index.Add(i);
        for (int i = min_index.Count - 1;i > 0;i--)
            if (min_index[i] == min_index[i - 1] + 1)
                min_index[i] = -1;
        List<int> l = new List<int>();
        foreach (var i in min_index)
            if (i != -1)
                l.Add(i);
        int ans = int.MaxValue;
        foreach (var i in l){
#if TEST
            Console.WriteLine(i);
#endif
            int c = 0;
            long[] cp = new long[n];
            for (int k = 0;k < n;k++)
                cp[k] = a[k];
            for (int j = i - 1;j >= 0;j--){
                long ri = Math.Abs(cp[j + 1]);
                long le = cp[j];
                int x = Math.Max((int)Math.Log(ri/(le + 0.0),2.0),0);
                cp[j] *= (long)Math.Pow(2.0,x) * (x % 2 == 1 ? -1 : 1);
                c += x;
                while (cp[j] > cp[j + 1]){
                    cp[j] *= -2;
                    c++;
                }
            }
            for (int j = i + 1;j < n;j++){
                int x = Math.Max(0,(int)Math.Log(cp[j - 1]/(cp[j] + 0.0),2.0));
                c += x;
                cp[j] *= (long)Math.Pow(2.0,x) * (x % 2 == 1 ? -1 : 1);
                while (cp[j] < cp[j - 1]){
                    cp[j] *= -2;
                    c ++;
                }
            }
#if TEST
            foreach (var j in cp)
                Console.Write("{0} ",j);
            Console.WriteLine();
#endif
            ans = Math.Min(ans,c);
        }
        Console.WriteLine(ans);
    }
}