For the circuit shown, the counter state (Q₁ Q₀) follows the sequence

In the following circuit, X is given by

The Boolean expression Y= $$\overline A \,\overline B \,\overline C \,D + \overline A BC\overline D + A\overline {B\,} \overline C \,D + AB\overline C \,\overline D $$

The Boolean function Y=AB+CD is to be realized using only 2-input NAND gates. The minimum number of gates required is