In one of Santa's research laboratories, the scientists have discovered a new chemical element and have named it Xmasium (by analogy with the famous elements Rubidium, Caesium, and Francium). Xmasium exists in three different types: There is α-Xmasium, β-Xmasium, and γ-Xmasium. If two Xmasium-atoms of different type collide, they sometimes merge into a single atom of the third type. If two Xmasium-atoms of the same type collide, they repel each other and nothing else happens.
Ruprecht puts 91 α-Xmasium-atoms, 25 β-Xmasium-atoms, and 4 γ-Xmasium-atoms into a cooking pot, covers it, and then leaves for lunch. When he returns, he notices that all Xmasium-atoms in the pot now are of the same type.
What is the largest possible number z of Xmasium-atoms in the pot at that moment?