#!/usr/bin/env python3
from fractions import Fraction
# 0=1,1=-1,2=i,3=-i,4=j,5=-j,6=k,7=-k
# element as (kind,sign); kind 0=scalar,1=i,2=j,3=k
tab={}
tab[(1,1)]=(0,-1)
tab[(2,2)]=(0,-1)
tab[(3,3)]=(0,-1)
tab[(1,2)]=(3,1)
tab[(2,1)]=(3,-1)
tab[(2,3)]=(1,1)
tab[(3,2)]=(1,-1)
tab[(3,1)]=(2,1)
tab[(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]
dp={}
for e,(q,a,b) in enumerate(letters):
    dp[(e,e,q,a,b)]=1
for pos in range(1,12):
    nd={}
    for (f,l,q,x,y),c in dp.items():
        for g,(qq,aa,bb) in enumerate(letters):
            if g==inv[l]: continue
            key=(f,g,mul(q,qq),x+aa,y+bb)
            nd[key]=nd.get(key,0)+c
    dp=nd
S=0
N=0
for (f,l,q,x,y),c in dp.items():
    if l==inv[f]: continue
    if q!=(kind,sign) where (kind,sign)=(0,-1): pass
    if q!=(0,-1): continue
    if (x+2*y)%5: continue
    e=(abs(2*x-y)+abs(x+2*y)+abs(-3*x-y))//2
    S+=e*c
    N+=c
print(S,N,Fraction(S,24))