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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N = gets.to_i
a_list = gets.strip.split(/ /).collect{|n| n.to_i}

count_p_list = [0] * N
count_p = 0
prev_p = a_list[-1]
gap_p_list = []

count_n_list = [0, 1]
count_n = 1
prev_n = prev_p * -2
gap_n_list = []

(1...N).each{|i|
	a_p = a_list[N - 1 - i]
	while prev_p < a_p
		if gap_p_list.length > 0
			gap = gap_p_list[-1]
			gap_i, gap_n = gap
			count_p += (i - gap_i) * 2
			if gap_n == 1
				gap_p_list.pop
			else
				gap[1] = gap_n - 1
			end
		else
			count_p += i * 2
		end
		prev_p *= 4
	end
	n = 0
	t = 4
	while prev_p >= a_p * t
		t *= 4
		n += 1
	end
	if n > 0
		gap_p_list << [i, n]
	end
	prev_p = a_p
	count_p_list[N - 1 - i] = count_p
	
	a_n = a_list[i] * -2
	count_n += 1
	while prev_n > a_n
		if gap_n_list.length > 0
			gap = gap_n_list[-1]
			gap_i, gap_n = gap
			count_n += (i - gap_i) * 2
			if gap_n == 1
				gap_n_list.pop
			else
				gap[1] = gap_n - 1
			end
		else
			count_n += i * 2
		end
		prev_n *= 4
	end
	n = 0
	t = 4
	while prev_n < a_n * t
		t *= 4
		n += 1
	end
	if n > 0
		gap_n_list << [i, n]
	end
	prev_n = a_n
	count_n_list << count_n
}

#p count_p_list
#p count_n_list

min = nil
(0...N).each{|i|
	count = count_n_list[i] + count_p_list[i]
	if min == nil || count < min
		min = count
	end
}
puts min