Tournament

题意翻译

有 $n$ 个人，贿赂他的代价为 $a[i]$。这些人中，贿赂代价为 $-1$ 的是你的朋友。现在，你可以两两配对，使得编号小的被淘汰，但是，如果你贿赂了编号大的，那么编号大的被淘汰，而编号小的留下。问：使得你朋友夺得冠军的最小代价

题目描述

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?

输入输出格式

输入格式

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] $ .

输出格式

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

输入输出样例

输入样例 #1

4
3 9 1 -1

输出样例 #1

0

输入样例 #2

8
11 -1 13 19 24 7 17 5

输出样例 #2

12

说明

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 $ );