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: Time Limit Exceeded)

from math import log2, ceil


def _check(bbb):
    ret = 0
    pb = -1
    for b in bbb:
        if pb > b:
            d = ceil((pb - b) / 2) * 2
            ret += d
            b += d
        pb = b
    return ret


def check(x, bbb):
    ret = x
    ret += _check(bbb[x:])
    ret += _check(reversed(bbb[:x]))
    return ret


def solve(n, aaa):
    l = 0
    r = n
    bbb = list(map(log2, aaa))
    while l < r:
        m1 = (l + r) // 2
        m2 = m1 + 1
        res1 = check(m1, bbb)
        res2 = check(m2, bbb)
        # print(l, r, m1, m2, res1, res2)
        if res1 > res2:
            l = m1 + 1
        else:
            r = m1
    return check(r, bbb)


n = int(input())
aaa = list(map(int, input().split()))
print(solve(n, aaa))