A student performed displacement reactions using metals X, Y, Z and solutions of their ions, $X^{2+}$, $Y^{2+}$, $Z^{2+}$. The results are shown.
* $X(s) + Z^{2+}(aq) \rightarrow$ No reaction
* $Y(s) + X^{2+}(aq) \rightarrow$ No reaction
* $Z(s) + Y^{2+}(aq) \rightarrow$ Reaction occurs
What is the increasing order of the reactivity of X, Y and Z metals?