Recently Georgie has learned about polynomials. A polynomial in one variable
can be viewed as a formal sum
an-1xn-1 + … +
a1x + a0,
where x is the formal variable and ai are the coefficients of the polynomial.
The greatest i such that ai ≠ 0 is called the
degree of the polynomial. If ai = 0 for all i, the degree of the
polynomial is considered to be −∞.
If the degree of the polynomial is zero or −∞, it is called
trivial, otherwise it is called non-trivial.
What really impressed Georgie while studying polynomials
was the fact that in some cases one can
apply different algorithms and techniques developed for
integer numbers to polynomials.
For example, given two polynomials, one may sum them up, multiply them, or
even divide one of them by the other.
The most interesting property of polynomials, at Georgie's point of view, was
the fact that a polynomial, just like an integer number, can be factorized.
We say that the polynomial is irreducible if it cannot be represented
as the product of two or more non-trivial polynomials with real coefficients.
Otherwise the polynomial is called reducible.
For example, the polynomial x2-2x+1
is reducible because it can be represented as (x - 1) (x - 1),
while the polynomial x2+1 is not. It is well known
that any polynomial can be represented as the product of one or more irreducible
Given a polynomial with integer coefficients,
Georgie would like to know whether it is irreducible. Of course, he would also
like to know its factorization, but such problem seems to be too difficult for him
now, so he just wants to know about reducibility.
Input file format
The first line of the input file contains n — the degree of the polynomial.
Next line contains n + 1 integer numbers,
an, an-1, …, a1, a0 —
polynomial coefficients (an ≠ 0).
Output file format
Output YES if the polynomial given in the input file is irreducible
and NO in the other case.