Square

For the given function (F(x) = a_0 $\cdot$ f_0(b_0 $\cdot$ x) + ...+ a_n $\cdot$ f_n(b_n $\cdot$ x)), and for the specified values of (A) and (B), determine the area enclosed by the graphs of the functions (y = F(x)), (y = -C), (x = A), and (x = B). Here, (0 $\le$ n $\le$ 25), (-25 $\le$ a_i, b_i $\le$ 25), (b_i $\ne$ 0), (C = abs(a_0/b_0) + ...+ abs(a_n/b_n)), (-1000 $\le$ A, B $\le$ 1000), and each (f_i) is either (sin) or (cos).

Input

The input file begins with the values of (A) and (B), followed by a line containing (F(x)). This line contains no spaces, and (a_i) and (b_i) may be omitted, in which case their values should be assumed to be (1). Similarly, (-sin(-x)) should be interpreted as (-1 $\cdot$ sin(-1 $\cdot$ x)).

Output

The output file should contain a single line with the calculated area, formatted to a precision of 6 decimal places.

Examples