def triangle_type(a,b,c):
    """Checks arguments correlation with triangle sides:
    If any two sides are equal returns "Isosceles triangle",
    If the sum of any two arguments is less then the third one returns - "Not a triangle"
    If all arguments are different returns "Versatile triangle"
    If all arguments are equal returns "Equilateral triangle\""""
    if a < b + c and b < c + a and c < b + a:
        if a == b == c:
            return "Equilateral triangle"
        elif a == b != c or b == c != a or c == a != b:
            return "Isosceles triangle"
        elif a != b and b != c and c != a:
            return "Versatile triangle"
        else:
            return "Not a triangle"
    else:
        return "This triangle does not exist"