0115. Components of Connectivity

Input file name:	connect.in
Output file name:	connect.out
Time limit:	2 s
Memory limit:	64 megabytes

Your task is to find the number of components of connectivity of a real algebraic curve f(x, y)=0.

Input file

The total degree of the polynomial f(x, y) will not exceed 6, and all coefficients are integer numbers not exceeding 10⁴ by their absolute values. The exact representation of polynomials is given by the following BNF:

Different tokens of input (with the exception of digits forming a <number>) are separated by any number of space and/or newline characters.

Output file

Output the number of components.

Examples:

connect.in	connect.out
X^2 + Y^2 - 1	1
X^2 - Y^2 - 1	2
Y^2 - X^3 - X^22	1

Source: Petrozavodsk Summer 2003. Primary Contest, Sunday, August 24
Author: Andrew Lopatin, Nick Durov

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