# Well ordering of reals from linear ordering of power set of reals

Working without the axiom of choice (ZF or even ZF + DC), can we show the existence of a well ordering of the real line $\mathbb{R}$ assuming that there is a linear ordering of $\mathcal{P}(\mathbb{R})$? I know that we can construct a linear ordering of $\mathcal{P}(\mathbb{R})$ using a well ordering of $\mathbb{R}$. But I don't see how to prove the converse if it is possible at all.