#!/usr/bin/env python3⏎
⏎
"""⏎
This program calculates the nth Fibonacci number in O(log(n)).⏎
It's possible to calculate F(1_000_000) in less than a second.⏎
"""⏎
import sys⏎
from typing import Tuple⏎
⏎
⏎
def fibonacci(n: int) -> int:⏎
    """⏎
    return F(n)⏎
    >>> [fibonacci(i) for i in range(13)]⏎
    [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]⏎
    """⏎
    if n < 0:⏎
        raise ValueError("Negative arguments are not supported")⏎
    return _fib(n)[0]⏎
⏎
⏎
# returns (F(n), F(n-1))⏎
def _fib(n: int) -> Tuple[int, int]:⏎
    if n == 0:  # (F(0), F(1))⏎
        return (0, 1)⏎
⏎
    # F(2n) = F(n)[2F(n+1) − F(n)]⏎
    # F(2n+1) = F(n+1)^2+F(n)^2⏎
    a, b = _fib(n // 2)⏎
    c = a * (b * 2 - a)⏎
    d = a * a + b * b⏎
    return (d, c + d) if n % 2 else (c, d)⏎
⏎
⏎
if __name__ == "__main__":⏎
    n = int(sys.argv[1])⏎
    print(f"fibonacci({n}) is {fibonacci(n)}")⏎