def find_index_closing_parenthesis(string: str):
    """Find the index of the closing parenthesis"""
    assert string.startswith("("), "string has to start with '('"
    stack = []
    for index, letter in enumerate(string):
        if letter == "(":
            stack.append(letter)
        elif letter == ")":
            stack.pop()
            if not stack:
                return index

    raise SyntaxError(f"Transonic syntax error for string {string}")