Minimal sufficiency survives under a bijective relabelling

Suppose that $X_1$ and $X_2$ are independent random variables having Bernoulli distribution with mean $p$ and $2p$ respectively, where $0<p<1/2$. (I) $(X_1,X_2)$ is minimal sufficient for $p$. (II) $2X_1+5X_2$ is minimal sufficient for $p$.