import cmath

def fft(input):
  N=len(input)
  n=1
  M=0
  while N>n:
    M+=1
    n*=2
  if n != N: 
     print "size must be power of 2"
     return None
  N2=N/2
  output=[0]*N

#bit reversal
  j=0
  for i in range(N-1):
    output[j]=complex(input[i])
    b=N2
    while(b<=j):
      j=j-b
      b=b/2
    j=j+b
  output[N-1]=complex(input[N-1])

#twiddle factors
  stride2=1
  for i in range(M):
    q=0
    stride1=stride2
    stride2=2*stride1
    for k in range(stride1):
      a=cmath.exp(-1j*q)
      q=q+cmath.pi/stride1
      for j in range(k,N,stride2):
        j2=j+stride1
        print j2,j,a
        temp=output[j2]*a
        output[j2]=output[j]-temp 
        output[j]=output[j]+temp 

  return output 

     


def invfft(input):
    output=fft([i.conjugate()/len(input) for i in input])
    return [i.conjugate() for i in output]


a=range(2048)
b=range(2048)
b.reverse()
input=a+b

print invfft(fft(input))