sort array with some of the elements in a known range
Using radix sort, the second subarray can be sorted in $\Theta(log_{b}(n\sqrt n)(n + b)$ where $b$ is the base with which the numbers are represented. If $n$ is chosen  as the base, radix sort sort the array in $\Theta(log_{n}(n\sqrt n)(n + n)) = \Theta(\frac{3}{2}(n + n)) = \Theta(n)$. Now all 3 subarrays can be sorted in $\Theta(n)$ thus the array is sorted in $\Theta(n)$