A circular array consists of $7$ points such that the distance between any two neighboring points along the circumference is $1$ unit distance. Two frogs are currently lying on the array.

Every second, each frog jumps to one of the adjacent points, with equal probability. Let $f(x)$ be the expected time after which both the frogs occupy the same position in the array if initially, they were $x$ unit distance apart.

You are required to find the value of $f(1)\cdot f(2)\cdot f(3)$.