Very simple roots

A polynomial

$p(x) = x^n + a_{n-1}x^{n-1} + \cdots + a_2x^2 + a_1x + a_0$

of degree $n$ may be called simple if it satisfies the following conditions:

• All coefficients are integers
• Its $n$ roots $r_{0,1,\ldots,n-1}$ are all real and distinct
• For every root $r_i$ there is exactly one coefficient $a_j$ such that $r_i = a_j$ .

Does there exist a simple polynomial of degree $n \geq 1$ ?