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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		if(N == 1){
			Console.WriteLine(0);
			return;
		}
		
		int l = 0;
		int r = N - 1;
		while(r - l > 1){
			int c = (l + r) / 2;
			long t0 = calc(c);
			long t1 = calc(c+1);
			if(t1 > t0){
				l = c;
			} else {
				r = c;
			}
		}
		
		Console.WriteLine(calc(r));
	}
	
	long calc(int idx){
		
		long[] cnt = new long[N];
		
		for(int j=idx + 1;j<N;j++){
			long now = A[j];
			long prev = A[j - 1];
			
			cnt[j] = cnt[j - 1];
			if(now > prev){
				while(cnt[j] >= 2 && now > prev * 4){
					cnt[j] -= 2;
					now /= 4;
				}
			} else if(now < prev){
				while(now < prev){
					now *= 4;
					cnt[j] += 2;
				}
			}
		}
		
		for(int j=idx - 1;j >= 0;j--){
			long now = A[j];
			long prev = A[j + 1];
			
			cnt[j] = cnt[j + 1];
			if(cnt[j] % 2 == 1){
				now *= 2;
				prev *= 2;
				
				if(now > prev){
					while(cnt[j] >= 3 && now > prev * 4){
						cnt[j] -= 2;
						now /= 4;
					}
				} else if(now < prev){
					while(now < prev){
						now *= 4;
						cnt[j] += 2;
					}
				}
			} else {
				if(now > prev){
					cnt[j] = 1;
				}
			}
		}
		
		long tot = 0;
		for(int i=0;i<N;i++) tot += cnt[i];
		return tot;
		
	}
	
	
	
	int N;
	long[] A;
	public Sol(){
		N = ri();
		A = rla();
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}