P3680 [CERC2016] Convex Contour

Some geometric figures are arranged neatly from left to right in a single row on a square grid. They occupy a consecutive segment of one row, with exactly one figure in each cell. Each figure is one of the following three: 1. A square that exactly fills a single cell. 2. A circle inscribed in a single cell. 3. An equilateral triangle whose base coincides with the bottom edge of the cell.  The side length of each cell is $1$. Compute the perimeter of the convex hull of these figures.

The first line contains a positive integer $n$, the number of figures. The second line contains $n$ characters, describing each figure from left to right: `S` denotes a square, `C` denotes a circle, and `T` denotes an equilateral triangle.

Output a single real number, the perimeter of the convex hull. Your answer will be accepted if the absolute or relative error does not exceed $10^{-6}$.

For $100\%$ of the testdata, $1 \le n \le 20$. Translated by ChatGPT 5