Sets, Relations and Functions: JEE Main 2021 Mathematics question

If A = {x $\in$ R : |x $-$ 2| > 1}, B = {x $\in$ R : $\sqrt {{x^2} - 3}$ > 1}, C = {x $\in$ R : |x $-$ 4| $\ge$ 2} and Z is the set of all integers, then the number of subsets of the set (A $\cap$ B $\cap$ C)^c $\cap$ Z is ________________.