import cmath
# an in place implementation

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
  N2=N/2

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


#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=input[j2]*a
        input[j2]=input[j]-temp 
        input[j]=input[j]+temp 

  return

     


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

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

fft(input)
invfft(input)
print input