Area between a lattice path and its chord

Consider a path on the plane that starts at the origin and can move only up or right. The path is written as a string of 'U' and 'R' characters. 'U' moves one unit up and 'R' moves one unit to the right. In the figure below, the path given by the string RRRURRUUURRRRRUUR is drawn as a thick line.

Figure 1: a sample 2D path

Now draw the straight line that joins the origin to the last point of the path. It is the dotted line in the figure. Compute the total area that lies between this line and the path, shown in gray in the figure.

When the path crosses the line several times, add up the areas of all the separate regions. If the path consists only of 'R' or only of 'U', the line lies on top of the path and the area is $0$.

The input consists of one or more test cases, one per line. Each line holds a path string of one or more 'U' and 'R' characters, followed by the letter 'S'.

Every path in the input can be drawn on a grid of size $1000 \times 1000$. That is, one path contains at most $1000$ letters 'R' and at most $1000$ letters 'U'.

The last line of the input is a single 'S' and is not a test case.

For each test case, print the area on its own line. Round to three digits after the decimal point and always print all three digits.