A $30 \times 30$ grid of squares contains $900$ fleas, initially one flea per square.
When a bell is rung, each flea jumps to an adjacent square at random (usually $4$ possibilities, except for fleas on the edge of the grid or at the corners).

If the expected number of unoccupied squares after $3^N$ rings of the bell is $p/q$, where $\gcd(p,q)=1$. Find $(p \cdot q^{-1}) \bmod 1000000007$.