201305: [AtCoder]ARC130 F - Replace by Average

Problem Statement

Given is a sequence of $N$ positive integers $A = (A_1, A_2, \ldots, A_N)$.

You can do the following operation on this sequence any number of times.

• Choose integers $i, j, k$ such that $1\leq i < j < k \leq N$ and $j = \frac{i+k}{2}$. Replace $A_j$ with $\lfloor\frac{A_i+A_k}{2}\rfloor$.

Find the minimum possible value of $\sum_{i=1}^N A_i$ after the operations.

Constraints

• $3\leq N\leq 3\times 10^5$
• $1\leq A_i\leq 10^{12}$

Input

Input is given from Standard Input in the following format:

$N$
$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print the answer.

Sample Input 1

5
2 2 5 5 4

Sample Output 1

13

The following operations achieves $\sum_{i=1}^N A_i = 13$.

• Do the operation with $(i,j,k) = (1,3,5)$. The sequence $A$ is now $(2,2,3,5,4)$.
• Do the operation with $(i,j,k) = (3,4,5)$. The sequence $A$ is now $(2,2,3,3,4)$.
• Do the operation with $(i,j,k) = (2,3,4)$. The sequence $A$ is now $(2,2,2,3,4)$.

Sample Input 2

5
3 1 4 1 5

Sample Output 2

11

Sample Input 3

3
3 1 3

Sample Output 3

7

Sample Input 4

3
3 5 3

Sample Output 4

9