Divide and Conquer#5671
It is well known that points can divide the line into at most n + 1 parts, and lines can divide the plane into at most \dfrac{n^2 + n + 2}{2} parts. These facts have always impressed Buddy. But recently, he has learned about higher-dimensional spaces, and this impressed him much more!
Now Buddy wonders how many parts hyperplanes can divide -dimensional space into. His elder brother Dubby told him that for each , this number can be represented as a polynomial in with rational coefficients. Help him to find this polynomial.
The input file contains (1 \leq m \leq 18).
On the first line of the output file, print the degree of the polynomial. On the second line, output the coefficients of the polynomial, separated by spaces. Coefficients must be listed starting from the leading one. All coefficients must be printed as irreducible fractions. If some coefficient is negative, the minus sign must precede its numerator, not the denominator.
Example 1