In ancient times, three neighboring kingdoms — Antheon, Beelor, and Cicadale —were ruled by close friends.

To symbolize their friendship, they constructed three straight roads linking the kingdoms together. The first road connecting Antheon to Beelor had Statue of Unity exactly at the halfway of it. The second road connecting Beelor to Cicadale had Statue of Friendship exactly at the halfway of it. The third road connecting Antheon to Cicadale had Statue of Harmony exactly at the halfway of it.

For example, if Antheon is located at $$$(1,2)$$$, Beelor at $$$(3,6)$$$ and Cicadale at $$$(7,4)$$$, then:

• Statue of Unity would be at $$$(\frac{1+3}{2},\frac{2+6}{2})=(2,4)$$$.
• Statue of Friendship would be at $$$(\frac{3+7}{2},\frac{6+4}{2})=(5,5)$$$.
• Statue of Harmony would be at $$$(\frac{1+7}{2},\frac{2+4}{2})=(4,3)$$$.

Figure G.1: Illustration of the location of the kingdoms and the statues corresponding to the example above

Tragically, the kingdoms were eventually wiped out by a devastating onslaught of pesticides, leading to their complete destruction. Yet, the three ancient statues somehow withstood the test of time, standing as the only surviving remnants of these lost civilizations.

Now, an archaeologist is determined to find the original locations of these lost kingdoms. He believes that the statues hold the clues to uncovering where the kingdoms once were. Your task is to help him figure out the locations of the kingdoms based on the positions of the surviving statues.