We are given a sequence a1 ... an. We can manipulate this sequence using the operation reduce(i), which replaces elements ai and ai+1 with a single element max(ai, ai+1), resulting in a new shorter sequence. The cost of this operation is max(ai, ai+1). After n−1 operations reduce, we obtain a sequence of length 1. Our task is to compute the cost of the optimal reducing scheme, i.e. the sequence of reduce operations with minimal cost leading to a sequence of length 1.

Input

The first line contains n (1 ≤ n ≤ 1,000,000), the length of the sequence. The following n lines contain one integer ai, the elements of the sequence (0 ≤ ai ≤ 1,000,000,000).

Output

In the first and only line of the output print the minimal cost of reducing the sequence to a single element.

Example

Input:
3
1
2
3

Output:
5