Solving recurrence relation $T(n) \leq \sqrt{n}T(\sqrt{n}) + n$


Given the condition: $ T(O(1)) = O(1)$ and $ T(n) \leq \sqrt{n}T(\sqrt{n}) + n$ . I need to solve this recurrence relation. The hardest part for me is the number of subproblems $ \sqrt{n}$ is not a constant, it’s really difficult to apply tree method and master theorem here. Any hint? My thought is that let $ c = \sqrt{n}$ such that $ c^2 = n$ so we have $ T(c^2) \leq cT(c) + c^2$ but I does not look good.