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.

4
3 1 4 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 $-6, 1, 4, 4$.

5
1 2 3 4 5

0

$A_1 \leq A_2 \leq ... \leq A_N$ holds before any operation is performed.

8
657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097

7