Let n be a natural number, n ≤ 8. Consider the following equation:</p>

xⁿ + c_n-1x^n-1 + c_n-2x^n-2 + … + c₁x + c₀ = 0

where c_n-1, c_n-2, …, c₁, c₀ are integers and c₀ ≠ 0.

It is known that all the n roots of the equation are real numbers. We consider that each root r of the equation satisfies the condition: -10 ≤ r ≤ 10. Also, there might be roots that appear more than once.

Find the number of irrational roots of the equation (an irrational root is a root that is an irrational number).

입력 형식

The input file contains a single test. The first line of the input file contains the value of n. The second line contains the values of c_n-1, c_n-2, …, c₁, c₀: each two consecutive values are separated by a single space.

출력 형식

The result will be written to standard output.

예제 입력

6
12 -12 -454 -373 3754 1680

예제 출력

2