from typing import Optional, Union


def normaliser_type_tiers(type_tiers: Union[str, int, None]) -> Optional[str]:
    if type_tiers is None:
        return None

    mapping_int = {0: "client", 1: "fournisseur", 2: "prospect", 3: "all"}

    if isinstance(type_tiers, int):
        return mapping_int.get(type_tiers, "all")

    if isinstance(type_tiers, str) and type_tiers.isdigit():
        return mapping_int.get(int(type_tiers), "all")

    return type_tiers.lower() if isinstance(type_tiers, str) else None