Let $f: [0, \infty) \to \mathbb{R}$ be a function satisfying the following conditions:

(1) For any $x, y \geq 0$, $f(x+y) \geq f(x)+f(y)$.

(2) For any $x \in [0, 2]$, $f(x) \geq x^2 – x$.

Prove that, for any positive integer $M$ and positive reals $n_1, n_2, \cdots, n_M$ with $n_1 + n_2 + \cdots + n_M = M$, we have

$$f(n_1) + f(n_2) + \cdots + f(n_M) \geq 0.$$