E. Tournament
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are organizing a boxing tournament, where $$$n$$$ boxers will participate ($$$n$$$ is a power of $$$2$$$), and your friend is one of them. All boxers have different strength from $$$1$$$ to $$$n$$$, and boxer $$$i$$$ wins in the match against boxer $$$j$$$ if and only if $$$i$$$ is stronger than $$$j$$$.

The tournament will be organized as follows: $$$n$$$ boxers will be divided into pairs; the loser in each pair leaves the tournament, and $$$\frac{n}{2}$$$ winners advance to the next stage, where they are divided into pairs again, and the winners in all pairs advance to the next stage, and so on, until only one boxer remains (who is declared the winner).

Your friend really wants to win the tournament, but he may be not the strongest boxer. To help your friend win the tournament, you may bribe his opponents: if your friend is fighting with a boxer you have bribed, your friend wins even if his strength is lower.

Furthermore, during each stage you distribute the boxers into pairs as you wish.

The boxer with strength $$$i$$$ can be bribed if you pay him $$$a_i$$$ dollars. What is the minimum number of dollars you have to spend to make your friend win the tournament, provided that you arrange the boxers into pairs during each stage as you wish?

Input

The first line contains one integer $$$n$$$ ($$$2 \le n \le 2^{18}$$$) — the number of boxers. $$$n$$$ is a power of $$$2$$$.

The second line contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$, where $$$a_i$$$ is the number of dollars you have to pay if you want to bribe the boxer with strength $$$i$$$. Exactly one of $$$a_i$$$ is equal to $$$-1$$$ — it means that the boxer with strength $$$i$$$ is your friend. All other values are in the range $$$[1, 10^9]$$$.

Output

Print one integer — the minimum number of dollars you have to pay so your friend wins.

Examples
Input
4
3 9 1 -1
Output
0
Input
8
11 -1 13 19 24 7 17 5
Output
12
Note

In the first test case no matter how you will distribute boxers into pairs, your friend is the strongest boxer and anyway wins the tournament.

In the second test case you can distribute boxers as follows (your friend is number $$$2$$$):

$$$1 : 2, 8 : 5, 7 : 3, 6 : 4$$$ (boxers $$$2, 8, 7$$$ and $$$6$$$ advance to the next stage);

$$$2 : 6, 8 : 7$$$ (boxers $$$2$$$ and $$$8$$$ advance to the next stage, you have to bribe the boxer with strength $$$6$$$);

$$$2 : 8$$$ (you have to bribe the boxer with strength $$$8$$$);