The nth Cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial of largest degree with integer coefficients that is a divisor of x^n − 1, and is not a divisor of x^k − 1 for any k < n.



Task

 Find and print the first 30 cyclotomic polynomials.
 Find and print the order of the first 10 cyclotomic polynomials that have n or -n as a coefficient.


See also
 Wikipedia article, Cyclotomic polynomial, showing ways to calculate them.
 The sequence A013594 with the smallest order of cyclotomic polynomial containing n or -n as a coefficient.
 
for(n=1,30,print(n," : ",polcyclo(n)))
 
contains_coeff(n, d) = p=polcyclo(n);for(k=0,poldegree(p),if(abs(polcoef(p,k))==d,return(1)));return(0)
 
for(d=1,10,i=1; while(contains_coeff(i,d)==0,i=i+1);print(d," : ",i))
 