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.

Input

Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N

Output

Print the answer.

Constraints

• $1 \leq N \leq 200000$
• $1 \leq A_i \leq 10^9$

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

见题面 Input 部分

见题面 Output 部分