import math

def fib(n):
  ar = [0, 1]
  if n < len(ar):
    return ar[n]
  else:
    while n > len(ar)-1:
      ar.append(
        ar[len(ar)-1] + ar[len(ar)-2]
      )
    return ar[n]

def find_fib(sum):
  if sum < fib(500):
    n = 0
    while True:
      if fib(n) > sum:
        return -1 # This is an error code
      elif fib(n) < sum:
        n = n+1
      else:
        return n
  else:
    return find_fib_formula(sum)

# For sums greater than n=500 because the previous function will be too slow
def find_fib_formula(sum):
  if sum <= fib(1000):
    Phi = (math.sqrt(5) + 1)/2
    formula_result = round(math.log((sum * math.sqrt(5)), Phi))
    if fib(formula_result) == sum:
      return formula_result
    else:
      return -1
  else:
    return find_big_fib(sum)

# For sums greater than n=1000 because Python can't handle the int->float conversion
def find_big_fib(sum):
  Phi = (math.sqrt(5) + 1)/2
  possible_solution =  round(math.log(sum * 2, Phi))
  if fib(possible_solution) == sum:
    return possible_solution
  else:
    possible_solutions = [
      possible_solution - 1,
      possible_solution - 2,
      possible_solution - 3,
      possible_solution + 1,
      possible_solution + 2,
      possible_solution + 3,
    ]
    for i in possible_solutions:
      if fib(i) == sum:
        return i
    return -1

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