Winding number of points on a path

Question

I know that for $|z| = 1$ circular path with counter-clockwise rotation, the winding number of any point within the circle is 1(or more if the path is circulated more than 1 time. and also negative if the rotation is clockwise). But what if the point was on the path? what would be the winding number then. Thus I am curious about 2 cases:

1. Winding number of p when p is on the $|z| = 1$ circle(counter-clockwise).

2. Winding number of p when p is on the $|z| = 1$ circle and also there is another $|z| = 2$ circle. Both counter-clockwise direction and

3. Same as 2, but for opposite directions.