## Find the tight upper bound of $\sum_{i=1}^n \frac{i}{i+x_i}$, where the $x_i$’s are distinct in $\{1,2,…,n\}$

What is the tight upper bound of $$\sum_{i=1}^n \frac{i}{i+x_i}$$, where the $$x_i$$‘s are distinct integers in $$\{1,2,…,n\}$$?