Balance

Many forces act on a sailboat, which lets it sail in many directions even when the wind is not blowing the way the sailor wants to go. For the boat to be easy to steer, though, certain forces must be balanced.

Suppose the wind blows from the north and the boat faces west. Above the water, the wind hits the angled sails and pushes the boat to the southwest. The keel reaches deep below the water, and the water's resistance on the keel creates a counterforce pushing the boat northward. Ideally, the northward force on the keel cancels the southward component of the force on the sails, so the boat moves due west.

A problem arises if the centre of the sails — the Centre of Effort, or CE — is not directly above the centre of the keel — the Centre of Lateral Resistance, or CLR. The boat can pivot about the centre of the keel. If the sails are too far forward of the keel, the wind pushes the bow (front) southward and the boat turns south. If the sails are too far aft of (behind) the keel, the wind pushes the stern (back) southward and the boat turns north. When the sails and keel are balanced, the boat sails in a straight line.

In this problem you examine a side view of the boat to decide whether the CE is above the CLR. The CE is the centroid of the part of the boat above the waterline, and the CLR is the centroid of the part below the waterline. The centroid of a polygon is its centre of area — equivalently, the centre of mass of a uniform flat plate of that shape.

The first line contains a single integer $n$, the number of points on the outline of the side view of the boat. Each of the next $n$ lines contains two integers, the $x$ and $y$ coordinates of a point on the outline. The points are given in order around the outline. The $x$-axis (the line $y = 0$) is the waterline. The boat faces in the direction of increasing $x$.

If the CE is forward of the CLR, print:

CE is forward of CLR by N units.

If the CE is aft of (behind) the CLR, print:

CE is aft of CLR by N units.

In both cases replace N with the difference between the $x$-coordinates of the CE and the CLR, written to exactly two decimal places. If the $x$-coordinates of the CE and the CLR are equal, print:

Balanced.