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