Initially, there are $$3^{80}$$ particles at the origin $$(0, 0)$$. At each step the particles are moved to points above the x-axis as follows: if there are $$n$$ particles at any point $$(x, y)$$, then $$\frac{n}{3}$$ of them are moved to $$(x+1,y+1)$$, $$\frac{n}{3}$$ are moved to $$(x,y+1)$$ and the remaining to $$(x-1,y+1)$$. For example, after the first step, there are $$3^{79}$$ particles each at $$(1, 1)$$, $$(0, 1)$$ and $$(-1, 1)$$. After the second step, there are $$3^{78}$$ particles each at $$(2, 2)$$ and $$(-2, 2)$$, $$2\cdot 3^{78}$$ particles each at $$(1, 2)$$ and $$(-1, 2)$$, and $$3^{79}$$ particles at $$(0, 2)$$. After $$80$$ steps, the number of particles at $$(79, 80)$$ is: