#!/usr/bin/env python3
"""
Prime Factorization Tool - Compute prime factors of a positive integer.

Usage: python prime_factorizer.py <number>
Exit 0: success, prints factors
Exit 1: error (invalid input, negative number, or 1)
"""

import sys
from typing import List


def prime_factors(n: int) -> List[int]:
    """Return the prime factorization of n as a list of prime factors."""
    if n < 2:
        return []
    
    factors = []
    d = 2
    while d * d <= n:
        while n % d == 0:
            factors.append(d)
            n //= d
        d += 1
    if n > 1:
        factors.append(n)
    return factors


def main():
    if len(sys.argv) != 2:
        print("Usage: python prime_factorizer.py <positive_integer>", file=sys.stderr)
        sys.exit(1)
    
    try:
        n = int(sys.argv[1])
        if n < 1:
            print("Error: Number must be positive", file=sys.stderr)
            sys.exit(1)
        if n == 1:
            print("1 has no prime factors")
            sys.exit(0)
        
        factors = prime_factors(n)
        if len(factors) == 1:
            print(f"{n} = {factors[0]} (prime)")
        else:
            factor_str = " x ".join(str(f) for f in factors)
            print(f"{n} = {factor_str}")
        
        sys.exit(0)
    except ValueError:
        print("Error: Invalid integer", file=sys.stderr)
        sys.exit(1)


if __name__ == "__main__":
    main()