Contest Duration: - (local time) (120 minutes)
E - Negative Doubling /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

N 個の正の整数 A_1, A_2, ..., A_N があります． 高橋君は，これらの整数に対して，次の操作を好きな回数行うことができます：

• 1 \leq i \leq N を選び，A_i の値を -2 倍にする．

マイナス 2 倍であることに注意してください．

制約

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

入力

N
A_1 A_2 ... A_N


入力例 1

4
3 1 4 1


出力例 1

3


• i=4 を選び，A_4 の値を -2 倍にする．A_1, A_2, A_3, A_4 はそれぞれ 3, 1, 4, -2 になる．
• i=1 を選び，A_1 の値を -2 倍にする．A_1, A_2, A_3, A_4 はそれぞれ -6, 1, 4, -2 になる．
• i=4 を選び，A_4 の値を -2 倍にする．A_1, A_2, A_3, A_4 はそれぞれ -6, 1, 4, 4 になる．

入力例 2

5
1 2 3 4 5


出力例 2

0


入力例 3

8
657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097


出力例 3

7


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


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