Bin Fruits By Price

fruit_prices is a dictionary with fruit names as keys and prices as values.

Write bin_fruits(fruit_prices) that classifies every fruit into one of three categories and returns a dictionary with exactly the keys 'cheap', 'affordable' and 'costly' in that order:

• cheap -- price less than 3 (not inclusive)
• affordable -- price between 3 and 6 (both inclusive)
• costly -- price greater than 6 (not inclusive)

Each value is the list of fruits in that category, kept in the order in which they appear in fruit_prices (a list, so the result is deterministic). All three keys must be present even when a category is empty.

Example

bin_fruits({'Apple': 2, 'Banana': 4, 'Kiwi': 8}) returns {'cheap': ['Apple'], 'affordable': ['Banana'], 'costly': ['Kiwi']}.

Your task

Implement this function:

def bin_fruits(fruit_prices: dict) -> dict:

Write the function only — the arguments are read for you and the return value is printed automatically.

Arguments arrive as one Python literal per line, in this order: fruit_prices.

Example

Input

{'Apple': 2, 'Banana': 4, 'Kiwi': 8}

Output

{'cheap': ['Apple'], 'affordable': ['Banana'], 'costly': ['Kiwi']}