# coding=utf-8

# 1000-digit Fibonacci number
# Problem 25
# https://projecteuler.net/problem=25
#
# The Fibonacci sequence is defined by the recurrence relation:
# Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
# Hence the first 12 terms will be:
# F1 = 1
# F2 = 1
# F3 = 2
# F4 = 3
# F5 = 5
# F6 = 8
# F7 = 13
# F8 = 21
# F9 = 34
# F10 = 55
# F11 = 89
# F12 = 144
# The 12th term, F12, is the first term to contain three digits.
# What is the index of the first term in the Fibonacci sequence to contain 1000 digits?

from math import log10, ceil, sqrt

def main():
	print(nDigitFibonacci(900))
	print(nDigitFibonacci(1000))

def nDigitFibonacci(digits):
	return ceil((log10(10) * (digits - 1) + log10(5) / 2) / log10((1 + sqrt(5)) / 2))

if __name__ == '__main__':
	main()
