import numpy as np




def FFT_backup(inp):
  inp = np.array(inp)
  out = np.fft.fft(inp)
  out = [val for val in np.abs(out)]
  print(out)
  return out


def FFT_real(inp):
  inp = np.array(inp)
  out = FFT(inp)
  out = [val for val in np.abs(out)]
  print(out)
  return out


def FFT(inp):
  return FFT_np(inp)

def FFT_np(inp):
  inp = np.array(inp)
  N = inp.shape[0]
  if N == 1:
    return inp
  X_even = FFT_np(inp[::2])
  X_odd  = FFT_np(inp[1::2])
  k = np.arange(N // 2)
  tw = np.exp(-2j * np.pi * k / N) * X_odd
  return np.concatenate((X_even + tw, X_even - tw))