#include <iostream>
#include <math.h>
using namespace std;

double __forceinline GetMinMaxX1(double a,double b, double c, double d, double e, double f)
{
    return (4*c*d - 2*b*e - sqrt((-4*c*d + 2*b*e)*(-4*c*d + 2*b*e) -
        4*(b*b - 4*a*c)*(e*e - 4*c*f)))/(2.*(b*b - 4*a*c));
}
double __forceinline GetMinMaxX2(double a,double b, double c, double d, double e, double f)
{
    return (4*c*d - 2*b*e + sqrt((-4*c*d + 2*b*e)*(-4*c*d + 2*b*e) -
        4*(b*b - 4*a*c)*(e*e - 4*c*f)))/(2.*(b*b - 4*a*c));
}

int __forceinline GetMinX(double a,double b, double c, double d, double e, double f)
{
    return static_cast<int>(floor(min(GetMinMaxX1(a,b,c,d,e,f),GetMinMaxX2(a,b,c,d,e,f))));
}

int __forceinline GetMaxX(double a,double b, double c, double d, double e, double f)
{
    return static_cast<int>(ceil(max(GetMinMaxX1(a,b,c,d,e,f),GetMinMaxX2(a,b,c,d,e,f))));
}

double __forceinline GetLower(double a,double b, double c, double d, double e, double f, double x)
{
    return (-e - b*x - sqrt((e + b*x)*(e + b*x) - 4*c*(f + d*x + a*x*x)))/(2*c);
}

double __forceinline GetUpper(double a,double b, double c, double d, double e, double f, double x)
{
    return (-e - b*x + sqrt((e + b*x)*(e + b*x) - 4*c*(f + d*x + a*x*x)))/(2*c);
}

bool __forceinline IsInt(double i)
{
    static double intpart;
    return modf(i, &intpart) == 0.0;
}

bool __forceinline IsEllipse(double a,double b, double c, double d, double e, double f)
{
    return (b*b-4*a*c) < 0;
}

bool __forceinline IsEvaluable(double a,double b, double c, double d, double e, double f, double x)
{
    return ((e + b*x)*(e + b*x) - 4*c*(f + d*x + a*x*x)) >= 0;
}

int __forceinline GetNumLatticePoints(double a, double b, double c, double d, double e, double f)
{
    if(!IsEllipse(a,b,c,d,e,f))
        return 0;

    int iMin = GetMinX(a,b,c,d,e,f);
    int iMax = GetMaxX(a,b,c,d,e,f);
    int iLattice = 0;

    for(int i = iMin; i <= iMax; ++i)
    {
        double x = static_cast<double>(i);
        if(IsEvaluable(a,b,c,d,e,f,x))
        {
            double dLower = GetLower(a,b,c,d,e,f,x);
            double dUpper = GetUpper(a,b,c,d,e,f,x);
            if(IsInt(dLower))
                ++iLattice;
            if(dLower != dUpper && IsInt(dUpper))
                ++iLattice;
        }
    }
    return iLattice;
}

int main()
{
    for(double a = -20; a <= 20; ++a)
    {
        for(double b = -20; b <= 20; ++b)
        {
            for(double c = -20; c <= 20; ++c)
            {
                for(double d = -20; d <= 20; ++d)
                {
                    for(double e = -20; e <= 20; ++e)
                    {
                        for(double f = -20; f <= 20; ++f)
                        {
                            if(GetNumLatticePoints(a,b,c,d,e,f) == 17)
                            {
                                cout << "a = " << a <<  "; b = " << b << "; c = " << c << "; d = " << d << "; e = " << e << "; f = " << f << endl;
                            }
                        }
                    }
                }
            }
        }
    }
    system("pause");
}