Silhouette Perimeter

You are given a list of non-negative integers representing the heights of a sequence of buildings aligned side by side. The task is to compute the total perimeter of the silhouette formed when viewing the buildings from a distance.

The perimeter is calculated by summing:

• The left side of the first building and the right side of the last building,
• The top side of each building (which has length equal to the building's height),
• The absolute differences between the heights of adjacent buildings (which represent the partially exposed vertical sides).

In mathematical form, if the building heights are given by \(h_1, h_2, \dots, h_n\), then for \(n \ge 1\), the perimeter \(P\) is computed as:

[ P = h_1 + h_n + \sum_{i=1}^{n} h_i + \sum_{i=2}^{n} |h_i - h_{i-1}|. ]

If there are no buildings (i.e. the list is empty), the perimeter is defined to be 0.

inputFormat

The input is provided via standard input (stdin) and consists of two lines.

• The first line contains a single integer \(n\) \( (n \ge 0)\) indicating the number of buildings.
• If \(n > 0\), the second line contains \(n\) space-separated non-negative integers representing the heights of the buildings.

outputFormat

Output a single integer to standard output (stdout) representing the total perimeter of the silhouette.

## sample

0

0