#!/usr/bin/env python3
from itertools import product
tab={(1,1):(0,-1),(2,2):(0,-1),(3,3):(0,-1),(1,2):(3,1),(2,1):(3,-1),(2,3):(1,1),(3,2):(1,-1),(3,1):(2,1),(1,3):(2,-1)}
def mul(a,b):
    if a[0]==0: return (b[0],a[1]*b[1])
    if b[0]==0: return (a[0],a[1]*b[1])
    k,s=tab[(a[0],b[0])]
    return (k,a[1]*b[1]*s)
letters=[((1,1),2,1),((1,-1),-2,-1),((2,1),-1,2),((2,-1),1,-2)]
inv=[1,0,3,2]
for d in (4,6):
    cnt=sm=0
    for u in product(range(4),repeat=d):
        if any(u[(i+1)%d]==inv[u[i]] for i in range(d)): continue
        q=(0,1);x=y=0
        for e in u:
            qq,a,b=letters[e]
            q=mul(q,qq);x+=a;y+=b
        ok=(y%5==0)
        if d==4: ok=ok and q==(0,-1)
        if d==6: ok=ok and q[0]==3
        if ok:
            ee=(abs(x)+abs(y)+abs(-x-y))//2
            cnt+=1;sm+=ee*(12//d)
    print(d,cnt,sm)