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)

try:
    n = int(input())
    a = list(map(int, input().split()))
#    print(a)
    i = 0
    count = 0
    while (i < n - 1):
        if a[i] <= a[i+1]:
            i += 1
        elif i == 0:
            a[i] = a[i] * -2
#            print(a)
            count += 1
        else:
            # print(a[i+1] * -2, 10 **9)
            # print(a[i+1] * -2 > 10 **9)
            if a[i+1] * -2 > 10 **9:
                count = -1
                break
            else:
                a[i+1] = a[i+1] * -2
#                print(a)
                count += 1

    print(count)
except EOFError:
    pass