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: Accepted)

def f(A, s):
    X = [0] * N
    q = []
    a = 0
    for i in range(N):
        b = a
        X[i] = X[i-1]
        a = A[i]
        if a * s < 0:
            X[i] += 1
            a *= -2

        if i == 0:
            continue
            
        r = b/a
        while r >= 4:
            q.append(i)
            r /= 4

        while r < 1:
            X[i] += 2 * (i - (0 if len(q) == 0 else q.pop()))
            r *= 4
            
    return X

N = int(input())
A = [int(a) for a in input().split()]
X = f(A,-1)
Y = f(A[::-1],1)

mi = min(X[-1], Y[-1])
for i in range(N-1):
    mi = min(mi, X[i] + Y[-2-i])
print(mi)