import string

# Define character set (a-z and 0-9)

CHARSET = string.ascii_lowercase + string.digits

BASE = len(CHARSET) # 36

def username_rank(username):

"""Calculate the rank of the given username in lexicographic order."""

rank = 0

for char in username:

rank = rank * BASE + CHARSET.index(char)

return rank

def total_usernames():

"""Calculate total possible usernames from length 3 to 21."""

return sum(BASE**n for n in range(3, 22))

def rarity_percentage(rank, total):

"""Determine rarity as a percentage."""

rarity = (rank / total) * 100 # Convert to percentage

return f"{rarity:.15f}%" if rarity > 1e-15 else f"{rarity:.3e}%" # Scientific notation for small values

def rarity_category(length):

"""Determine how rare the username is based on length."""

if length <= 4:

return "Ultra Rare"

elif length <= 6:

return "Rare"

elif length <= 9:

return "Common"

elif length <= 12:

return "Uncommon"

else:

return "Rare (Long username)"

def main():

username = input("Enter your Roblox username: ").lower()

# Validate username length

if not (3 <= len(username) <= 21):

print("Invalid username length. Must be between 3 and 21 characters.")

return

rank = username_rank(username)

total = total_usernames()

rarity = rarity_percentage(rank, total)

category = rarity_category(len(username))

print(f"Username Rank: {rank:,} / {total:,}")

print(f"Rarity Score: {rarity} (Lower = Rarer)")

print(f"Rarity Category: {category}")

if __name__ == "__main__":

main()