Given the following functional dependencies
$\left\{X \rightarrow W, X \rightarrow Y, Y \rightarrow Z, Z \rightarrow PQ\right\}$
Consider the $FD$ set implied using above $FD$ set.
Implied $FD$ set = $\left\{X \rightarrow Z, X \rightarrow WY, X \rightarrow WZ, X \rightarrow YQ, Y \rightarrow P \right\}$
The number of functional dependencies in implied $FD$ set are invalid are ______________.