Alice and Bob are playing a number guessing game.

Alice has secretly chosen an integer . Bob can ask Alice any integer , and Alice will respond with either Yes or No, indicating whether . Additionally, Alice keeps track of the cost of each query, which is . Note that Bob is unaware of the specific cost associated with each query.

Bob knows that must be one of the integers that are given in ascending order. To determine , Bob wants to minimize the worst-case scenario of the sum of query costs.

Please determine the minimum possible sum of query costs in the worst-case scenario.

The first line contains a positive integer .
The second line contains  positive integers , guaranteed to be sorted in ascending order.

Output one integer, which is the minimum sum of query costs in the worst-case scenario.

4
1 5 6 7

4

10
8 18 20 24 50 53 77 92 100 121

64

.