How to change style for ttk OptionMenu including the dropdown selection?

Question

I want to edit the font of the OptionMenu including the dropdown selection, but I don't know how to do that for the dropdown selection.

I tried to change the ttk style, but that only affects the main button, not the dropdown selection.

import tkinter as tk
from tkinter import ttk

root = tk.Tk()

# style changes
style = ttk.Style()
style.configure(".", font=("Arial", 20)) # larger font for everything
style.configure("TMenubutton", background="darkgray") # background for menubutton 

menu = ttk.OptionMenu(root, tk.StringVar(), "North", *["North", "East", "South", "West"])
menu.grid()

root.mainloop()

With the following result: OptionMenu