import re

def is_email(identifier: str) -> bool:
    return re.match(r"[^@]+@[^@]+\.[^@]+", identifier) is not None

def is_phone(identifier: str) -> bool:
    """
    Validate phone number format. Supports:
    - International format: +1234567890, +91-9876543210
    - National format: 9876543210, (123) 456-7890
    - With/without spaces, dashes, parentheses
    """
    # Remove all non-digit characters except +
    cleaned = re.sub(r'[^\d+]', '', identifier)
    
    # Check if it's a valid phone number (8-15 digits, optionally starting with +)
    if re.match(r'^\+?[1-9]\d{7,14}$', cleaned):
        return True
    return False

def validate_identifier(identifier: str) -> str:
    """
    Validate and return the type of identifier (email or phone).
    Raises ValueError if neither email nor phone format.
    """
    if is_email(identifier):
        return "email"
    elif is_phone(identifier):
        return "phone"
    else:
        raise ValueError("Identifier must be a valid email address or phone number")