Irrational Roots

You are given a natural number $n$ and integers $c_{n-1}, c_{n-2}, \dots, c_1, c_0$. Consider the equation

$x^n + c_{n-1}x^{n-1} + c_{n-2}x^{n-2} + \dots + c_1x + c_0 = 0$

where $c_0 \neq 0$, all $n$ roots of the equation are real, and every root $r$ satisfies $-10 \le r \le 10$. The same value may occur as a root more than once.

Write a program that counts how many of the $n$ roots are irrational. Roots are counted with multiplicity, so an irrational root that occurs three times counts as 3.

The first line contains $n$. ($1 \le n \le 8$)

The second line contains $c_{n-1}, c_{n-2}, \dots, c_1, c_0$ in that order, separated by single spaces.

Print the number of irrational roots on one line.