def isLegalTriangle(s1: float, s2: float, s3: float) -> bool:
    """Return True if s1, s2, and s3 can form a legal triangle, False otherwise."""
    return s1 + s2 > s3 and s2 + s3 > s1 and s3 + s1 > s2


def getTriangleType(a: float, b: float, c: float) -> str:
    """Return the type of triangle formed by sides a, b, and c."""
    if not isLegalTriangle(a, b, c):
        return "illegal"
    if a == b and b == c:
        return "equilateral"
    elif a == b or b == c or c == a:
        return "isosceles"
    else:
        return "scalene"


print("Testing getTriangleType()...", end="")
assert getTriangleType(5, 6, 7) == "scalene"
assert getTriangleType(7, 5, 6) == "scalene"
assert getTriangleType(6, 5, 5) == "isosceles"
assert getTriangleType(5, 6, 5) == "isosceles"
assert getTriangleType(5, 5, 6) == "isosceles"
assert getTriangleType(7, 7, 7) == "equilateral"
assert getTriangleType(1, 2, 3) == "illegal"
print("Passed!")