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 Python (3.4.3) (judge verdict: Wrong Answer)

n=int(input())
a=list(map(int,input().split()))
l,r=0,n+1
def g(x):
    c=1
    while x//4!=0:
        x=(x-x%4)//4
        c+=1
    return c
def f(x):
    c=x
    p=0
    if x>1:
        for i in range(x-2,-1,-1):
            if i!=n-1:
                if a[i+1]>a[i]:
                    p+=g(a[i+1]//a[i]+1)*2
            c+=p
    if x<n:
        p=0
        for i in range(x,n-1):
            if a[i+1]<a[i]:
                p+=g(a[i+1]//a[i]+1)*2
            c+=p
    return c
while r-l>2:
    s=(2*l+r)//3
    t=(l+2*r)//3
    if f(s)>f(t):
        l=s
    else:
        r=t
print(min(f(l),f(r),f(r-1)))