Dropdown menu in React js

I am currently building a dropdown based design in React. When I click any one of the buttons, the dropdown appears. Now when I click anywhere inside the dropdown, I want the dropdown to stay. But based on my current implementation, when I click on the dropdown, the dropdown goes away. I can fix this behaviour by prop drilling but the code gets ugly. How can I implement this cleanly?

export default function SearchFilter() {
  const [selected, setSelected] = useState(null);

  const handleClick = (e) => {
    const id = e.target.id;
    setSelected(id);
    }
  };
  const clearSelected = (e) => {
    if (e.target.id) return;
    setSelected(null);
  };
  useEffect(() => {
    window.addEventListener("click", clearSelected);
    return () => window.removeEventListener("click", clearSelected);
  });
  return (
    <div onClick={handleClick}>

      <MenuItem id={1} className={selected == 1 ? "shadow-xl" : ""}>

          <MenuDropdown className={`absolute left-0 top-full translate-y-3 ${
            selected != 1 && "hidden" />

      </MenuItem>

      <MenuItem id={2} className={selected == 2 ? "shadow-xl" : ""} />
      <MenuItem id={3} className={selected == 3 ? "shadow-xl" : ""} />
    </div>
  );
}