# Spin_{2n}/Spin_{2n-1}: Lambda_T = even-sum lattice in Z^n, W = W(D_n), theta = diag(-1,1,..,1), phi(x)=2x_1 eps_1, u := y(2 eps_1)
# L = D_{n-1} on coordinates 2..n, 2rho_L = (0, 2(n-2), 2(n-3), ..., 2, 0); shift q^{rho_L}: x^mu -> t^{<2rho_L,mu>} u^{mu_1}
import sys
from itertools import permutations, product
from collections import Counter
n=int(sys.argv[1])
two_rhoL=[0]+[2*(n-1-i) for i in range(1,n)]
def orbit(mu):  # W(D_n): permutations and even sign changes
    out=set()
    for perm in permutations(mu):
        for signs in product([1,-1],repeat=n):
            if signs.count(-1)%2==0: out.add(tuple(s*x for s,x in zip(signs,perm)))
    return out
def restrict(mu):
    res={}
    for nu in orbit(mu):
        res.setdefault(nu[0],Counter())[sum(a*b for a,b in zip(two_rhoL,nu))]+=1
    return res
for mu in [(1,1)+(0,)*(n-2),(2,)+(0,)*(n-1),(1,1,1,1)+(0,)*(n-4) if n>=4 else None]:
    if mu is None: continue
    R=restrict(mu)
    print('n=%d, mu=%s: r(m_mu) = sum_k u^k * (coeff):'%(n,mu))
    for k in sorted(R): print('   u^%d :'%k, dict(sorted(R[k].items())),' (t-exponents -> counts)')