Factoring a Polynomial

A polynomial in one variable can be written as the formal sum $a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0$, where $x$ is the formal variable and the numbers $a_i$ are its coefficients. The largest index $i$ with $a_i \neq 0$ is called the degree of the polynomial; if $a_i = 0$ for every $i$, the degree is defined to be $-\infty$. A polynomial whose degree is $0$ or $-\infty$ is called trivial; any other polynomial is non-trivial.

A polynomial with real coefficients is called irreducible if it cannot be written as a product of two or more non-trivial polynomials with real coefficients; otherwise it is called reducible. For instance, $x^2 - 2x + 1$ is reducible because $x^2 - 2x + 1 = (x - 1)(x - 1)$, whereas $x^2 + 1$ is irreducible. It is a classical fact that every polynomial can be written as a product of one or more irreducible polynomials.

Given a polynomial with integer coefficients, determine whether it is irreducible over the real numbers.

The first line contains the degree $n$ of the polynomial ($0 \le n \le 20$).

The second line contains $n + 1$ integers $a_n, a_{n-1}, \ldots, a_1, a_0$ — the coefficients of the polynomial ($-1000 \le a_i \le 1000$, $a_n \neq 0$).

Print YES if the polynomial is irreducible over the real numbers, and NO otherwise.