Negative Doubling

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.

Examples

Input

4 3 1 4 1

Output

3

Input

5 1 2 3 4 5

Output

0

Input

8 657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097

Output

7

inputFormat

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N

outputFormat

Output

Print the answer.

Examples

Input

4 3 1 4 1

Output

3

Input

5 1 2 3 4 5

Output

0

Input

8 657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097

Output

7

样例

4
3 1 4 1

3