import math

def primes_up_to(n: int):
    """Generate all primes ≤ n using sieve of Eratosthenes."""
    if n < 2:
        return []
    sieve = [True] * (n + 1)
    sieve[0] = sieve[1] = False
    for p in range(2, int(math.isqrt(n)) + 1):
        if sieve[p]:
            step = p
            start = p * p
            sieve[start:n + 1:step] = [False] * ((n - start) // step + 1)
    return [i for i, is_p in enumerate(sieve) if is_p]

def factor_exponents(n: int):
    """Return dict {prime: exponent} for n (n ≥ 1)."""
    exps = {}
    if n <= 1:
        return exps
    limit = math.isqrt(n)
    for p in primes_up_to(limit):
        if p * p > n:
            break
        while n % p == 0:
            exps[p] = exps.get(p, 0) + 1
            n //= p
    if n > 1:  # leftover prime
        exps[n] = exps.get(n, 0) + 1
    return exps

def exponents_in_prime_order(n: int, min_len=7):
    """
    Produce exponents in order [2, 3, 5, 7, 11, 13, ...],
    padded with zeros to length >= min_len.
    """
    if n == 1:
        return [0] * min_len

    exps = factor_exponents(n)

    # generate primes in ascending order until we cover all factors
    primes_needed = sorted(exps.keys())
    max_prime = max(primes_needed) if primes_needed else 2
    primes_list = primes_up_to(max_prime)

    out = [exps.get(p, 0) for p in primes_list]

    # pad with zeros
    while len(out) < min_len:
        out.append(0)

    return out

def format_exponents(exps):
    """Format as comma-separated list with zero-padded width=3."""
    return ",".join(f"{e:03d}" for e in exps)

def main():
  for s in range(1,100):
    #s = input("Enter a positive integer (1..10000000): ").strip()
    try:
        n = int(s)
    except ValueError:
        print("Error: please enter an integer.")
        return
    if n < 1 or n > 10_000_000:
        print("Error: number must be between 1 and 10,000,000.")
        return

    exps = exponents_in_prime_order(n, min_len=7)
    print(s, ': ',format_exponents(exps))

if __name__ == "__main__":
    main()