A special solution for a functional inequality from $\mathbb{R}\times \mathbb{R} $ onto $\mathbb{R}$

Question

Is there a bijection solution $\eta:\mathbb{R}\times \mathbb{R}\rightarrow \mathbb{R}$ (with an explicit formula, if it is possible) for the inequality $$\min\{x,y\}\leq \eta(x,y)\leq \max\{x,y\}\;\; ; \;\; x\neq y?$$