Problem Statement  
The theory of elliptic curves is involved with finding the number and properties of rational points  that is, points whose x and y values are rational numbers  and studying relationships between them. Elliptic curves, however, are curves of the form y^2 + ay + b = x^3 + cx^2 + dx + e. You feel that this type of equation is a bit too restrictive, and so you're going to generalize things a bit. Given a String equation, and two ints xmax and ymax, find the number of lattice points (x,y) that satisfy equation and such that 0 <= x <= xmax and 0 <= y <= ymax. Lattice points are those with both coordinates being integers. The string representing the equation follows the format "f(y)=g(x)", in more detail below:
Equation := Function(y) "=" Function(x) (Function(x) is analogous to Function(y).) If there are terms in a given function that are of the same power, consider their coefficients to be added together. For example, the equation "9y^3+5y^3=3+6" would be equivalent to "14y^3=9" (except that the latter is not in proper form and is thus illegal as input). Note that no term of the form "Nx^0" will be allowed, to prevent ambiguity regarding 0^0.  
Definition  
 
Notes  
  For C++ coders, the 64bit integer type is long long (a gcc extension).  
Constraints  
  xmax will be between 0 and 1000000, inclusive  
  ymax will be between 0 and 1000000, inclusive  
  equation will be between 3 and 50 characters, inclusive  
  equation will follow the form "f(y)=g(x)" given above  
  no y between 0 and ymax, inclusive, will cause f(y) to exceed 2^63  1  
  no x between 0 and xmax, inclusive, will cause g(x) to exceed 2^63  1  
  no term of the form Nx^0 will be allowed in the input.  
  no term of the form Ny^0 will be allowed in the input.  
Examples  
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