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Let n be a natural number, n ≤ 8. Consider the following equation:
xn + cn-1xn-1 + cn-2xn-2 + … + c1x + c0 = 0
where cn-1, cn-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).
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 cn-1, cn-2, …, c1, c0: each two consecutive values are separated by a single space.
The result will be written to standard output.
6 12 -12 -454 -373 3754 1680