struct Complex
{
double r,i;
Complex(double _r,double _i):r(_r),i(_i){}
Complex(){}
Complex operator +(const Complex &b)
{
return Complex(r+b.r,i+b.i);
}
Complex operator -(const Complex &b)
{
return Complex(r-b.r,i-b.i);
}
Complex operator *(const Complex &b)
{
return Complex(r*b.r-i*b.i,r*b.i+i*b.r);
}
};
void change(Complex y[],int len)
{
int i,j,k;
for(i = 1, j = len/2;i < len-1;i++)
{
if(i < j)swap(y[i],y[j]);
k = len/2;
while( j >= k)
{
j -= k;
k /= 2;
}
if(j < k)j += k;
}
}
void fft(Complex y[],int len,int on)
{
change(y,len);
for(int h = 2;h <= len;h <<= 1)
{
Complex wn(cos(-on*2*pi/h),sin(-on*2*pi/h));
for(int j = 0;j < len;j += h)
{
Complex w(1,0);
for(int k = j;k < j+h/2;k++)
{
Complex u = y[k];
Complex t = w*y[k+h/2];
y[k] = u+t;
y[k+h/2] = u-t;
w = w*wn;
}
}
}
if(on == -1)
for(int i = 0;i < len;i++)
y[i].r /= len;
}