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: Accepted)

N,*A=`dd`.split.map &:to_i
x,y=[A,A.reverse].map{|_|
	t=[]
	r=[c=0]
	_.each_with_index{|a,i|
		b=a
		q=1
		while !t.empty?&&t[-1][0]<b
			x,d,n=t.pop
			(c+=n*2;x*=4;d*=4)while x<b
			b=d
			q+=n
		end
		t<<(t.empty? ? [a,0,q] : [a,b,q])
		r<<c
	}
	r
}
p (0..N).map{|i|x[i]+i+y[-1-i]}.min