Platforms

On the planet Olympia, a set of sightseeing platforms hangs motionless at various heights above a river. Each platform is a point in a vertical plane and is described by two coordinates: the x-coordinate is its horizontal distance from the river's source, and the y-coordinate is its height above the water. No platform sits directly above another, so all x-coordinates are distinct.

The platforms are to be reused as launch stations for hang gliders. A glider may fly from one platform to another only when both of the following hold:

• It may only go to a platform of lower or equal height (the destination's $y$ is at most the current height).
• It may never fly against the river's flow: it may only go to a platform farther from the source (a strictly larger x-coordinate).

A route is a sequence of consecutive flights: from one platform to the next, then to the next, and so on. A route is called popular when it makes the greatest possible number of consecutive flights; the individual flight lengths do not matter.

Your task is to determine which platforms belong to at least one popular route.

The first line contains the number of test cases $T$.

Each test case begins with a line containing the number of platforms $N$ ($1 < N < 123456$). Each of the next $N$ lines contains two non-negative integers, the x- and y-coordinates of one platform. All x-coordinates within a test case are distinct.

For each test case, print a group of two lines.

The first line contains two integers: the number of flights in a popular route, and the total number of platforms that belong to at least one popular route.

The second line lists, in ascending order and separated by single spaces, the x-coordinates of those platforms.

If no flight is possible at all, the first line is 0 0 and the second line is empty.