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In [376]:

    
from KBs import *
class kb_2dntca():
    def __init__(self):
        self.familyname='2dntca'
        pass
    def rulestr2alias(self, rulestr):
        '''
        Convert a 26-digit hexadecimal rulestring to a B/S alias
        '''
        OUT = ''
        # rulestr =  '000000000060031c61c67f86a0'
        r=hex2bin(rulestr,102);
        r=r[::-1];
        rule=[i for i,x in enumerate(r) if x=='1'];
#         print r
        lst = [hensellist[i] for i in rule]
        lst.sort()
        
        #### group by B/S
        d = collections.OrderedDict((('b',{}),('s',{}))) ### set default
#         d = {'b':{},'s':{}}   ### set default
        d.update(
            {k:list(gp) for k,gp in itertools.groupby(lst, lambda x:x[0])}        
        )
        for k,lst in d.items():
            d[k] = {k:list(gp) for k,gp in itertools.groupby(lst, lambda x:x[1])}
            
        for bs, dd in d.items():
            OUT += bs
            for k,lst in dd.items():
                OUT += k + ''.join( conf[-1] for conf in lst)
        OUT = OUT.replace('_','')
        alias = OUT
        return alias


    def alias2rulestr(self,alias): 
        '''
        Convert a B/S alias to a 26-digit hexadecimal rulestring
        '''
    # alias.replace('-','')
        alias = re.sub('(\d-[a-zA-Z]+)',lambda o:invert(o.group()),alias)
        alias = p_NOTnumletter.sub( '', alias).lower()
        OUT = ['0']*102
        d = collections.OrderedDict((('b',{}),('s',{}))) ### set default
        # d.update()
        # alias.split('s')
        s = alias
        lst = [x for x  in re.split("([bs])", s) if x]
        if len(lst) % 2: #### Padding to even length
            lst += ['']
        d  = dict(ntuple(lst,2))
        idxs = []
        for k, v in d.items():
            s = v
            lst = [x for x in re.split("(\d)", s) if x]
            L  = len(lst)
            v_old = ''
            for i,v in enumerate(lst):
                if v.isdigit():
                    if v_old.isdigit():
                        idx = [henselidx.get( k + v_old + c,None) for c in subconf]
                        idxs.extend(idx)
                    if i + 1 == L:
                        idx = [henselidx.get( k + v + c,None) for c in subconf]
                        idxs.extend(idx)
                    num = v
                else:
                    idx = [henselidx[ k + num + v_i]  for v_i in v ]
                    idxs.extend(idx)
                v_old = v
        idxs = [ x for x in idxs if x is not None] 
        for i in idxs:
            if not i is None:
                OUT[i] = '1'
        bitstr=''.join(OUT[::-1]);
        hexstr=hex(int(bitstr,2)).lstrip('0x').rstrip('L').zfill(26)
        return hexstr
    def rulestr2adv(self,rulestr):
        ruleprj=np.array( 
            list(hex2bin(rulestr,102)[::-1]),
            np.int);
        adv = self.bin2adv(ruleprj)
#         ruleprj=np.array(list(hex2bin(rulestr,102)[::-1]));
#         fir=(2**np.arange(0,9)).reshape([1,3,3]);
#         pj=rca2ntca;
#         def adv(a,horizon):
#             return ruleprj[pj[convolve_int(a,fir,'wrap').astype(np.int)]]
#         # adv=lambda a, horizon: ruleprj[pj[convolve_int(a,fir,'wrap').astype(np.int)]]
        return adv 
    def conv(self,IN):
        '''
        Convovle using non-totalistic isotropic filter
        '''
        fir=(2**np.arange(0,9)).reshape([1,3,3]);
        pj=rca2ntca;
        return pj[convolve_int(IN,fir,'wrap').astype(np.int)]
    def bin2adv(self, ruleprj):
        if isinstance(ruleprj,str):
            ruleprj = list(ruleprj)
        ruleprj = np.array(ruleprj,np.int)
        def adv(a,horizon=0):
            return ruleprj[self.conv(a)]
        return adv
    def rstr(self,callback=(lambda x:bin2hex(x).zfill(26)) ):
        r = '{:0102b}'.format(random.randrange(2**102))
        if callback is not None:
            r = callback(r)
        return r
    def randadv(self):
        return self.bin2adv(self.rstr(None))
    def bulk_rstr(self,seed = 0,bsize=2**18,**kwargs):
        random.seed(seed)
        lst = [{'family':self.familyname,
                'rulestr':self.rstr(**kwargs)} for x in range(bsize)]
        return lst    
class kb_eca():
    def conv(self,IN,method):
        '''
        Convolve using 1D universal (non-totalistic non-isotropic) filter
        '''
        fir = (2**np.arange(3)).reshape([1,3,1])
        return convolve_int(IN,fir,method)
    def rstr(self,):
        pass
    def bin2adv(self,rulebin,method='wrap'):
        if isinstance(rulebin,str):
            rulebin = list(rulebin)
        rulebin = np.array(rulebin,np.int)
        def adv(a,horizon=0,method=method):
            return rulebin[self.conv(a,method=method)]
        return adv
    def rulestr2alias(self,rstr):
        assert len(rstr)==8
        alias = int(rstr,2)
        return str(alias)
    def alias2rulestr(self,alias):
        rstr = base2bin(alias,10,8)[::-1]
        return rstr
    def rulestr2adv(self,rstr):
        return self.bin2adv(rstr)
        
def sample(self,ini=None,adv = None,T = None):
    '''
    Sample an iterator ('CA_sys' object)
    '''
    if T is None:
        T = self.hmax
    if adv is None:
        adv = self.adv
    if ini is None:
        ini=self.rdf().astype(int)
    avc = ini
    hist = np.zeros((T+1,)+avc.shape,dtype=np.int)
    for i in range(T+1):
        hist[i]=avc
        avc=(adv(avc)) 
    return hist
def showsptime(arr,ax=None,**kwargs):
    if ax is None:
        fig,ax = plt.subplots(1,1,figsize=[12,4])
    
    return ax.pcolormesh(sflatten(arr),**kwargs)
kb  = kb_eca()
rstr = '11001010'
alias = kb.rulestr2alias(rstr)
print 'alias of mapper %s:'%rstr,alias
print 'rulestring of rule 110:',kb.alias2rulestr('110')

random.seed(0)
np.random.seed(30)
env = CA_sys()
env.family= kb_eca()
env.alias = '110'
env.alias = '118'
env.alias2rulestr()
env.change_size((1,100,40**2))
hist = sample(env,T=20)
# hist.shape
out = np.take(hist,0,axis=-1)
showsptime(out[::-1])
# print out
# showsptime(out)
plt.grid()
plt.show()









    



alias of mapper 11001010: 202
rulestring of rule 110: 01110110



In [2]:

    
# import os
# import re
# def DIR2lasti(DIR,pattern='seed(\d+)_size600'):
#     dlst = os.listdir(DIR)
#     dlst = ''.join(dlst)
#     it = re.findall(pattern,dlst)
#     lasti = max(map(int,it))
#     return lasti
# DIR = 'data_pdist/'
# DIR2lasti(DIR)

# import numpy as np
# fs = os.listdir(DIR)
# out = sum((np.load(os.path.join(DIR,f)).tolist()  for f in fs),[])



In [2]:

    
glider = '00011101100'
ini = np.reshape(map(int,glider),(1,-1,1))
out = sample(env,ini=ini,)
showsptime(np.squeeze(out).T)
plt.show()



In [3]:

    
glider = '10011010100101010010101010101000011'
ini = np.reshape(map(int,glider),(1,-1,1))
out = sample(env,ini=ini,)
showsptime(np.squeeze(out).T)
plt.show()



In [397]:

    
print cmp(0,1)

-1



In [405]:

    
def get_parent_shape(avc,t):
    spdim = avc.shape[1:]
    pardim = list(x+t*2 for x in spdim)
    if spdim[-1] == 1:
        pardim[-1] = 1
#     pardim =tuple(x+t*2 if x!=1 else x for x in spdim)
    return tuple(pardim)

def findparent(avc,env,t=1,method='brute'):
    pardim = get_parent_shape(avc,t)
    nbit = np.prod(pardim)
    parent = itertools.product(*[range(2)]*nbit)
#     print len(list(parent))
    parent = np.reshape(list(parent),(2**nbit,)+pardim)
#     print parent.shape
    
    out = sample(env, ini = parent,T = t)
    bot = out[-1]
    
    realdim = [i for i,x in enumerate(bot.shape) if x!=1 and i!=0]
    for ax in realdim:
        bot= np.take(bot,range(t,bot.shape[ax]-t),axis=ax)
    res  = bot[:,None]
    targ = avc[None]
    graph = np.all(res == targ,axis=(-1,-2))
    return parent,graph

def glider2num(glider):
    ini = np.reshape(map(int,glider),(1,-1,1))
    fir = np.reshape(2**np.arange(ini.size),(1,-1,1))
    ini_int = convolve_int(ini,fir,'reflect').flat[(ini.size-1)//2]
    return ini_int

def main(glider,particle=None,per = 2,T=5,silent=1,findall=0):
    outlst = []
    if particle is None:
        particle = glider2num(glider)
    ini = np.reshape(map(int,glider),(1,-1,1))
    fir = np.reshape(2**np.arange(ini.size),(1,-1,1))
#     fir = np.reshape(2**np.arange(ini.size),(1,-1,1))
#     ini_int = convolve_int(ini,fir,'reflect').flat[(ini.size-1)//2]

    out = sample(env,ini=ini,)
#     showsptime(np.squeeze(out).T)
#     plt.show()

#     T = 7
    out = -.1*np.ones( get_parent_shape(ini,T) + (1+T,),dtype=np.float)
    # raise Exception()
    for t in range(0,T+1):
        if t ==0:
            parent = ini
            paridx = 0
        else:
            parent,paridx = findparent(ini,env,t = t)
        validPar = parent[np.ravel(paridx)]
        recur = convolve_int(validPar,fir,'wrap') == particle

        if per:
            move = cmp(per,0)*(t//abs(per))
#             print move
        else:
            move = 0
#         driftidx=  t + move + (parent[0].size-1)//2
        driftidx=  t + move + (+ini.size-1)//2
        obsidx = recur[:, driftidx]    
        if not silent:
            print recur.shape
            print np.shape(obsidx)
            print obsidx.mean()
        if findall:
            outlst.append(validPar)
        else:
            outlst.append(validPar[obsidx.ravel()])
        row = np.mean(recur,axis=0)
        idx = range(T-t,T-t+len(row))
    #     out
    #     print row.shape
        if t==0:
            row = ini
        out[idx,:,t] = row
    #     break
    if not silent:
        showsptime(out.T)
        plt.show()
    res = outlst
#     print [np.shape(x) for x in res]
    tiles = [ {'parity':{'T':T,'per':per},
       'seq':tuple(sum(x,[]) ),} for x in np.array(res[T]).tolist()]        
    return tiles
#     return outlst
per  = 2
n = 5
lst = [base2bin(str(x),10,n) for x in range(2**n)]
# glider = '110011'
glider = '01110'
# if 1:
silent = 1
# for glider in lst:
# res = map(lambda x:main(x,per=1,T=4,silent=0),lst);
print 'Done'









    



Done



In [ ]:

    
%time



In [84]:

    
%time
n = 5
lst = [base2bin(str(x),10,n) for x in range(2**n)]
res = map(lambda x:main(x,per=0,T=3),lst);









    



CPU times: user 0 ns, sys: 0 ns, total: 0 ns
Wall time: 5.01 µs



In [85]:

    
res









    Out[85]:





[[{'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)}],
 [{'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1)}],
 [],
 [{'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1)}],
 [{'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1)}],
 [{'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1)}],
 [{'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0)},
  {'parity': {'T': 3, 'per': 0}, 'seq': (1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1)},
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In [88]:

    
%%time
####################################################################
####################################################################
####################################################################
#########oooo|oooo|xxx|cccc|oooo####################################
####################################################################
####################################################################
#########oooo|xxxc|ccc|oooo|oooo####################################
####################################################################
####################################################################
####################################################################
####################################################################
## source oooo->xxxx
## sink   cccc->oooo
## find paths from sources to sinks


# main(per=1,T=3)


import simpleCycles
### Look for a period 2 glider, drift 1 on a period 2 backgd
### common product is 6


Tbk = 3
tile0 = par2tiles(T=Tbk,per=0,n=1)

tile = tile0
curr = pre2curr(tile)
cks=simpleCycles.simple_cycles(adj2dct(tile2adj(tile0)))
# cks = list(cks)
cks = filter(lambda (i,x):len(x)==3,enumerate(cks))
# print 
print cks

ck = cks[0]
i,idx = ck
bkd = sum([curr[x] for x in idx],())
# tile
# print cks[0]
### 

### find period 2 static tiling
### at T=6 

p2T6tile = par2tiles(T=6,per=0,n=2)









    



[(47224, [22, 88, 80])]
CPU times: user 1.79 s, sys: 0 ns, total: 1.79 s
Wall time: 1.78 s



In [48]:



In [226]:

    
# %%time
Tb = 6
T = Tb
per = 2
dft = Tb/per
Lb = len(bkd)
print dft
print query
print len(query)
print 2*T
# bkdper = Tb / Tbk
# query = iter_head(itertools.cycle(bkd[::-1]),Tb)[::-1] + list(bkd) + iter_head(itertools.cycle(bkd),dft)


tile0 = main(glider=bkd,T=2*3,per=0)
curr = pre2curr(tile0)
tile0 = tile_flatten(tile0)
query = iter_head(itertools.cycle(bkd),Tb)
tile0Right = filter(lambda seq: tuple(seq[-Tb:])== tuple(query),tile0)

tileAll = tile_flatten(main(glider=bkd,T=2*3,per=0))
# print tile_flatten(tile0)[:5]

#### Do the right part first
#### Specify tail of the pattern

tile = tileAll[:]
print 'LEN,',len(tile)
for nper in range(1000):
    print nper
    L = T + nper*Lb
    if L > 2*T+Lb:
        break    
#         pass
    if nper:
        amat = tile2adj(tile_last,tile0Right,overlap=2*T)
        idx=  np.transpose(np.where(amat))
        tile = [tile_last[x]+bkd for x,y in idx]
    else:
        query = iter_head(itertools.cycle(bkd),L)
        f = lambda seq: tuple(seq[-L:]) == tuple(query)
        tile = filter(f,tile)    
    tile_last = tile
    
tileRight = tile_last
query = iter_head(itertools.cycle(bkd[::-1]),Tb)[::-1]
tile0Left = filter(lambda seq: tuple(seq[2:2+Tb])== tuple(query),tile0)









    



3
[0, 1, 1, 0, 1, 1]
6
12
LEN, 2816
0
1
2
3
4



In [455]:

    
query = iter_head(itertools.cycle(bkd[::-1]),Tb+Lb)[::-1]
tile = filter(lambda seq: tuple(seq[2:2+(Tb+Lb)])== tuple(query),tile0)
amat = tile2adj(tile)
# tile0Left = np.take(tile ,(amat.any(axis=1)),axis = 0)
# tile0Left = np.take(tile ,(amat.any(axis=1)),axis = 0)
# print query
tile0Left = np.array(tile)[amat.any(axis=1)]
tile0Left

# amat.any(axis=1)









    Out[455]:





array([[6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0],
       [6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1],
       [6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0],
       [6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1],
       [6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0],
       [6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1]])



In [621]:

    
tile0 = main(glider=bkd,T=2*3,per=0,findall=1)
curr = pre2curr(tile0)
tile0 = tile_flatten(tile0)

query = iter_head(itertools.cycle(bkd),Tb+Lb)
# print Tb,Lb
tile = filter(lambda seq: tuple(seq[-(Tb+Lb):])== tuple(query),tile0)
amat = tile2adj(tile)
tile0Right = np.array(tile)[amat.any(axis=1)]

query = iter_head(itertools.cycle(bkd[::-1]),Tb+Lb)[::-1]
tile = filter(lambda seq: tuple(seq[2:2+(Tb+Lb)])== tuple(query),tile0)
amat = tile2adj(tile)
tile0Left = np.array(tile)[amat.any(axis=0)]
# tile0Left = np.take(tile ,(amat.any(axis=0)),axis = 0)

query = iter_head(itertools.cycle(bkd),Tb)
tile = filter(lambda seq: tuple(seq[-(Tb):])== tuple(query),tile0)
amat = tile2adj(tile,tile0Right)
print amat.shape
tile = np.array(tile)[amat.any(axis=1)]
tile[:,1]=2
tile = tile.tolist()
tile = [x for x,_ in filter(lambda (x,y): tuple(x[2+Tb:-Tb])!=tuple(y),zip(tile,pre2curr(tile)))]
tileRight = tile

tileLeft = tile0Left

print len(tile0)
print len(tile0Right)
print len(tile0Left)
print len(tileRight)



In [506]:

    
printmat(tile)
print 
printmat(tileRight)
print 
printmat(tile0Right)









    



6,0,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1
6,0,0,0,0,0,0,0,1,1,0,0,1,1,0,1,1
6,0,0,0,0,0,0,0,1,1,1,0,1,1,0,1,1
6,0,0,0,0,0,0,1,0,1,1,0,1,1,0,1,1
6,0,0,0,0,0,0,1,1,1,0,0,1,1,0,1,1
6,0,0,0,0,0,1,0,0,0,1,0,1,1,0,1,1
6,0,0,0,0,0,1,0,0,1,1,0,1,1,0,1,1
6,0,0,0,0,0,1,0,1,1,0,0,1,1,0,1,1
6,0,0,0,0,0,1,0,1,1,1,0,1,1,0,1,1
6,0,0,0,0,0,1,1,0,1,1,0,1,1,0,1,1
6,0,0,0,0,1,0,0,0,0,1,0,1,1,0,1,1
6,0,0,0,0,1,0,0,0,1,1,0,1,1,0,1,1
6,0,0,0,0,1,0,0,1,1,0,0,1,1,0,1,1
6,0,0,0,0,1,0,0,1,1,1,0,1,1,0,1,1
6,0,0,0,0,1,0,1,0,1,1,0,1,1,0,1,1
6,0,0,0,0,1,0,1,1,1,0,0,1,1,0,1,1
6,0,0,0,0,1,1,0,0,0,1,0,1,1,0,1,1
6,0,0,0,0,1,1,0,0,1,1,0,1,1,0,1,1
6,0,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1
6,0,0,0,0,1,1,0,1,1,1,0,1,1,0,1,1
6,0,0,0,0,1,1,1,0,1,1,0,1,1,0,1,1
6,0,0,0,0,1,1,1,1,1,1,0,1,1,0,1,1
6,0,0,0,1,0,0,0,0,1,1,0,1,1,0,1,1
6,0,0,0,1,0,0,0,1,1,0,0,1,1,0,1,1
6,0,0,0,1,0,0,0,1,1,1,0,1,1,0,1,1
6,0,0,0,1,0,0,1,0,1,1,0,1,1,0,1,1
6,0,0,0,1,0,0,1,1,1,0,0,1,1,0,1,1
6,0,0,0,1,0,1,0,0,0,1,0,1,1,0,1,1
6,0,0,0,1,0,1,0,0,1,1,0,1,1,0,1,1
6,0,0,0,1,0,1,0,1,1,0,0,1,1,0,1,1
6,0,0,0,1,0,1,0,1,1,1,0,1,1,0,1,1
6,0,0,0,1,0,1,1,0,1,1,0,1,1,0,1,1
6,0,0,0,1,1,0,0,0,0,1,0,1,1,0,1,1
6,0,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1
6,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1
6,0,0,0,1,1,0,0,1,1,1,0,1,1,0,1,1
6,0,0,0,1,1,0,1,0,1,1,0,1,1,0,1,1
6,0,0,0,1,1,0,1,1,1,0,0,1,1,0,1,1
6,0,0,0,1,1,1,0,0,0,1,0,1,1,0,1,1
6,0,0,0,1,1,1,0,0,1,1,0,1,1,0,1,1
6,0,0,0,1,1,1,0,1,1,0,0,1,1,0,1,1
6,0,0,0,1,1,1,0,1,1,1,0,1,1,0,1,1
6,0,0,0,1,1,1,1,0,1,1,0,1,1,0,1,1
6,0,0,0,1,1,1,1,1,1,1,0,1,1,0,1,1
6,0,0,1,0,0,0,0,0,1,1,0,1,1,0,1,1
6,0,0,1,0,0,0,0,1,1,0,0,1,1,0,1,1
6,0,0,1,0,0,0,0,1,1,1,0,1,1,0,1,1
6,0,0,1,0,0,0,1,0,1,1,0,1,1,0,1,1
6,0,0,1,0,0,0,1,1,1,0,0,1,1,0,1,1
6,0,0,1,0,0,1,0,0,0,1,0,1,1,0,1,1
6,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1
6,0,0,1,0,0,1,0,1,1,0,0,1,1,0,1,1
6,0,0,1,0,0,1,0,1,1,1,0,1,1,0,1,1
6,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1
6,0,0,1,0,1,0,0,0,0,1,0,1,1,0,1,1
6,0,0,1,0,1,0,0,0,1,1,0,1,1,0,1,1
6,0,0,1,0,1,0,0,1,1,0,0,1,1,0,1,1
6,0,0,1,0,1,0,0,1,1,1,0,1,1,0,1,1
6,0,0,1,0,1,0,1,0,1,1,0,1,1,0,1,1
6,0,0,1,0,1,0,1,1,1,0,0,1,1,0,1,1
6,0,0,1,0,1,1,0,0,0,1,0,1,1,0,1,1
6,0,0,1,0,1,1,0,0,1,1,0,1,1,0,1,1
6,0,0,1,0,1,1,0,1,1,0,0,1,1,0,1,1
6,0,0,1,0,1,1,0,1,1,1,0,1,1,0,1,1
6,0,0,1,0,1,1,1,0,1,1,0,1,1,0,1,1
6,0,0,1,0,1,1,1,1,1,1,0,1,1,0,1,1
6,0,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1
6,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1
6,0,0,1,1,0,0,0,1,1,1,0,1,1,0,1,1
6,0,0,1,1,0,0,1,0,1,1,0,1,1,0,1,1
6,0,0,1,1,0,0,1,1,1,0,0,1,1,0,1,1
6,0,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1
6,0,0,1,1,0,1,0,0,1,1,0,1,1,0,1,1
6,0,0,1,1,0,1,0,1,1,0,0,1,1,0,1,1
6,0,0,1,1,0,1,0,1,1,1,0,1,1,0,1,1
6,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1
6,0,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1
6,0,0,1,1,1,0,0,0,1,1,0,1,1,0,1,1
6,0,0,1,1,1,0,0,1,1,0,0,1,1,0,1,1
6,0,0,1,1,1,0,0,1,1,1,0,1,1,0,1,1
6,0,0,1,1,1,0,1,0,1,1,0,1,1,0,1,1
6,0,0,1,1,1,0,1,1,1,0,0,1,1,0,1,1
6,0,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1
6,0,0,1,1,1,1,0,0,1,1,0,1,1,0,1,1
6,0,0,1,1,1,1,0,1,1,0,0,1,1,0,1,1
6,0,0,1,1,1,1,0,1,1,1,0,1,1,0,1,1
6,0,0,1,1,1,1,1,0,1,1,0,1,1,0,1,1
6,0,0,1,1,1,1,1,1,1,1,0,1,1,0,1,1
6,0,1,0,0,0,0,0,0,1,1,0,1,1,0,1,1
6,0,1,0,0,0,0,0,1,1,0,0,1,1,0,1,1
6,0,1,0,0,0,0,0,1,1,1,0,1,1,0,1,1
6,0,1,0,0,0,0,1,0,1,1,0,1,1,0,1,1
6,0,1,0,0,0,0,1,1,1,0,0,1,1,0,1,1
6,0,1,0,0,0,1,0,0,0,1,0,1,1,0,1,1
6,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,1
6,0,1,0,0,0,1,0,1,1,0,0,1,1,0,1,1
6,0,1,0,0,0,1,0,1,1,1,0,1,1,0,1,1
6,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,1
6,0,1,0,0,1,0,0,0,0,1,0,1,1,0,1,1
6,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,1
6,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,1
6,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,1
6,0,1,0,0,1,0,1,0,1,1,0,1,1,0,1,1
6,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,1
6,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,1
6,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1
6,0,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1
6,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,1
6,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,1
6,0,1,0,0,1,1,1,1,1,1,0,1,1,0,1,1
6,0,1,0,1,0,0,0,0,1,1,0,1,1,0,1,1
6,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,1
6,0,1,0,1,0,0,0,1,1,1,0,1,1,0,1,1
6,0,1,0,1,0,0,1,0,1,1,0,1,1,0,1,1
6,0,1,0,1,0,0,1,1,1,0,0,1,1,0,1,1
6,0,1,0,1,0,1,0,0,0,1,0,1,1,0,1,1
6,0,1,0,1,0,1,0,0,1,1,0,1,1,0,1,1
6,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,1
6,0,1,0,1,0,1,0,1,1,1,0,1,1,0,1,1
6,0,1,0,1,0,1,1,0,1,1,0,1,1,0,1,1
6,0,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1
6,0,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1
6,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1
6,0,1,0,1,1,0,0,1,1,1,0,1,1,0,1,1
6,0,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1
6,0,1,0,1,1,0,1,1,1,0,0,1,1,0,1,1
6,0,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1
6,0,1,0,1,1,1,0,0,1,1,0,1,1,0,1,1
6,0,1,0,1,1,1,0,1,1,0,0,1,1,0,1,1
6,0,1,0,1,1,1,0,1,1,1,0,1,1,0,1,1
6,0,1,0,1,1,1,1,0,1,1,0,1,1,0,1,1
6,0,1,0,1,1,1,1,1,1,1,0,1,1,0,1,1
6,0,1,1,0,0,0,0,0,1,1,0,1,1,0,1,1
6,0,1,1,0,0,0,0,1,1,0,0,1,1,0,1,1
6,0,1,1,0,0,0,0,1,1,1,0,1,1,0,1,1
6,0,1,1,0,0,0,1,0,1,1,0,1,1,0,1,1
6,0,1,1,0,0,0,1,1,1,0,0,1,1,0,1,1
6,0,1,1,0,0,1,0,0,0,1,0,1,1,0,1,1
6,0,1,1,0,0,1,0,0,1,1,0,1,1,0,1,1
6,0,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1
6,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1
6,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1
6,0,1,1,0,1,0,0,0,0,1,0,1,1,0,1,1
6,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1
6,0,1,1,0,1,0,0,1,1,0,0,1,1,0,1,1
6,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,1
6,0,1,1,0,1,0,1,0,1,1,0,1,1,0,1,1
6,0,1,1,0,1,0,1,1,1,0,0,1,1,0,1,1
6,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1
6,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1
6,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1
6,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1
6,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,1
6,0,1,1,0,1,1,1,1,1,1,0,1,1,0,1,1
6,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,1
6,0,1,1,1,0,0,0,1,1,0,0,1,1,0,1,1
6,0,1,1,1,0,0,0,1,1,1,0,1,1,0,1,1
6,0,1,1,1,0,0,1,0,1,1,0,1,1,0,1,1
6,0,1,1,1,0,0,1,1,1,0,0,1,1,0,1,1
6,0,1,1,1,0,1,0,0,0,1,0,1,1,0,1,1
6,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1
6,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,1
6,0,1,1,1,0,1,0,1,1,1,0,1,1,0,1,1
6,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,1
6,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1
6,0,1,1,1,1,0,0,0,1,1,0,1,1,0,1,1
6,0,1,1,1,1,0,0,1,1,0,0,1,1,0,1,1
6,0,1,1,1,1,0,0,1,1,1,0,1,1,0,1,1
6,0,1,1,1,1,0,1,0,1,1,0,1,1,0,1,1
6,0,1,1,1,1,0,1,1,1,0,0,1,1,0,1,1
6,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,1
6,0,1,1,1,1,1,0,0,1,1,0,1,1,0,1,1
6,0,1,1,1,1,1,0,1,1,0,0,1,1,0,1,1
6,0,1,1,1,1,1,0,1,1,1,0,1,1,0,1,1
6,0,1,1,1,1,1,1,0,1,1,0,1,1,0,1,1
6,0,1,1,1,1,1,1,1,1,1,0,1,1,0,1,1

6,0,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1
6,0,0,0,0,0,0,0,1,1,0,0,1,1,0,1,1
6,0,0,0,0,0,0,0,1,1,1,0,1,1,0,1,1
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6,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,1
6,0,1,1,1,1,0,0,0,1,1,0,1,1,0,1,1
6,0,1,1,1,1,0,1,0,1,1,0,1,1,0,1,1
6,0,1,1,1,1,1,0,0,1,1,0,1,1,0,1,1
6,0,1,1,1,1,1,1,0,1,1,0,1,1,0,1,1



In [653]:

    
def list2set(lst):
    return {tuple(x) for x in lst}
# A = list2set(tileLeft)
A=  list2set(tileRight)
B=  list2set(tileG)
print len(A)
print len(B)
A.update(B)
print len(A)



In [647]:

    
tile = tileLeft
print len(tile)
print len(set(tuple(x) for x in tile))



In [256]:

    
!pip install python-igraph --user









    



Collecting python-igraph
  Downloading python-igraph-0.7.1.post6.tar.gz (377kB)
    100% |████████████████████████████████| 378kB 1.7MB/s ta 0:00:01
Building wheels for collected packages: python-igraph
  Running setup.py bdist_wheel for python-igraph ... done
  Stored in directory: /home/shouldsee/.cache/pip/wheels/2b/9b/50/34d9d2b8f74c7a1c70f6337686d66f8fc8bbab6d2f196fe6ef
Successfully built python-igraph
Installing collected packages: python-igraph
Successfully installed python-igraph-0.7.1.post6
You are using pip version 9.0.1, however version 9.0.3 is available.
You should consider upgrading via the 'pip install --upgrade pip' command.



In [276]:

    
from igraph import Graph

# g = Graph.Lattice([10, 10], circular=False)
# g.get_all_shortest_paths(0)

def find_all_paths(graph, start, end):
    '''
    Source:https://stackoverflow.com/questions/2606018/path-between-two-nodes    
    '''
    def find_all_paths_aux(adjlist, start, end, path):
        path = path + [start]
        if start == end:
            return [path]
        paths = []
        for node in adjlist[start] - set(path):
            paths.extend(find_all_paths_aux(adjlist, node, end, path))
        return paths
    adjlist = [set(graph.neighbors(node)) for node in xrange(graph.vcount())]
    return find_all_paths_aux(adjlist, start, end, [])
# find









    Out[276]:





[[0]]



In [660]:

    
# tileG = tile_flatten(par2tiles(n=Lb,T=Tb,per=2))
tile = tile_flatten(par2tiles(n=Lb,T=Tb,per=2))
tile = [x for x,_ in filter(lambda (x,y): tuple(x[2+Tb:-Tb])!=tuple(y),zip(tile,pre2curr(tile)))]
tileG = tile
print len(tile)



In [666]:

    
# tile = tile0Right
# pre2curr(tileRight)
# [x[2+Tb:-Tb] for x in tile]



In [658]:

    
zip(tile,pre2curr(tile),[x[2+Tb:-Tb] for x in tile])









    Out[658]:





[((6, 2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (1, 0, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (1, 0, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (1, 0, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (1, 0, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (1, 0, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (1, 0, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (1, 0, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (1, 0, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0), (0, 0, 0), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (0, 0, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (0, 0, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 1), (0, 0, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (0, 0, 1), (0, 0, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 0, 0)),
 ((6, 2, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0), (0, 0, 1), (0, 0, 0)),
 ((6, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1), (0, 0, 1), (0, 0, 0)),
 ((6, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 0, 0)),
 ((6, 2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1), (0, 0, 1), (1, 0, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (1, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1), (0, 0, 1), (0, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (0, 0, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1), (0, 1, 1), (1, 1, 1)),
 ((6, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1), (0, 1, 1), (0, 0, 0)),
 ((6, 2, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0), (0, 1, 1), (1, 1, 0)),
 ((6, 2, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1), (0, 1, 1), (1, 1, 0)),
 ...]



In [718]:

    
tile = sum([ x.tolist() if not isinstance(x,list) else x  for x in 
            [tileLeft,tileRight,tileG]] ,
          [])
curr = pre2curr(tile,mid=1)

heads  = [x[2:2+2*T] for x in tile]
tails  = [x[-2*T:] for x in tile]
amat = np.array(tails)[:,None] == np.array(heads)[None,:]
print amat.shape
amat = np.all( amat,axis=-1)
# x.tolist()  for x in [tileLeft,tileRight,tileG]
# tile = np.vstack([tileLeft , tileRight , tileG])
# amat = tile2adj(tile)
g = Graph.Adjacency(amat.tolist())


# find_all_paths(g,0,1)
tLidx = range(len(tileLeft))
tRidx = range(len(tileLeft),len(tileLeft)+len(tileRight))
lst = []
res = map(lambda L: g.get_shortest_paths(L,tRidx),tLidx)
# for L,R in itertools.product(tLidx,tRidx):
#     p = g.get_shortest_paths(L,R)
#     lst += [p]
# print len(tileLeft)
# print len(tileLeft)+len(tileRight)









    



(4456, 4456, 12)



In [719]:









    



/home/shouldsee/.local/lib/python2.7/site-packages/ipykernel_launcher.py:5: RuntimeWarning: Couldn't reach some vertices at structural_properties.c:740
  """



In [709]:

    
print curr[1564]
printmat(sample(env,ini=np.reshape(tile[1564][2:],(1,-1,1)),T=6).squeeze())









    



(0, 0, 1)
0,0,0,0,0,1,0,0,1,1,0,0,1,1,0
0,0,0,0,1,1,1,1,0,1,1,1,0,1,1
1,0,0,1,0,0,0,1,1,0,0,1,1,0,1
1,1,1,1,1,0,1,0,1,1,1,0,1,1,0
0,0,0,0,1,1,1,1,0,0,1,1,0,1,1
1,0,0,1,0,0,0,1,1,1,0,1,1,0,1
1,1,1,1,1,0,1,0,0,1,1,0,1,1,0



In [714]:









    Out[714]:





[0, 1, 1]



In [734]:

    
out = [ x for x in res if sum( len(y) for y in x) !=0]
# out = [ x for x in out[0] if x]
out = out[1]
per = [x[1] for x in tile]
per_gb =  [sum(per[i] for i in x) for x in out]

# print per_gb
i = 82
ck = out[i]
ck = ck[0:1]*2 + ck + [0]*2
print ck 
printmat([tile[x][2:]for x in ck])
print [curr[x] for x in ck]
# print per_gb
print np.where(np.array(per_gb)>0)[0]
show_cycle( ck,curr)
# out[0]









    



[23, 23, 23, 25, 2294, 3309, 4219, 126, 0, 0]
0,1,1,0,1,1,0,1,1,0,1,1,0,1,1
0,1,1,0,1,1,0,1,1,0,1,1,0,1,1
0,1,1,0,1,1,0,1,1,0,1,1,0,1,1
0,1,1,0,1,1,0,1,1,0,1,1,1,0,1
0,1,1,0,1,1,0,1,1,1,0,1,1,1,0
0,1,1,0,1,1,1,0,1,1,1,0,1,1,1
0,1,1,1,0,1,1,1,0,1,1,1,0,1,1
1,0,1,1,1,0,1,1,1,0,1,1,0,1,1
0,1,1,0,1,1,0,1,1,0,0,0,0,0,0
0,1,1,0,1,1,0,1,1,0,0,0,0,0,0
[[0, 1, 1], [0, 1, 1], [0, 1, 1], [0, 1, 1], (0, 1, 1), (1, 0, 1), (1, 1, 0), [1, 1, 1], [0, 1, 1], [0, 1, 1]]
[ 21  22  23  26  44  49  50  51  54  68  77  78  82 100]
(101, 1, 30, 1)



In [402]:

    
tileG = tile_flatten(par2tiles(n=Lb,T=Tb,per=0))
print len(tileG)



In [411]:

    
# print(len(tileG))
cu = pre2curr(tileG)
i = 1000
print tileG[i],cu[i]









    



(6, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1) (0, 1, 1)



In [428]:

    
# tileG
tile = tileG
q = (6,2,1,1,0,1,1,0,1,1,0,1,1,1,0,1,1)
res = filter(lambda x:tuple(x)==q,tile)
print res









    



[(6, 2, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1)]



In [459]:

    
tileLeft









    Out[459]:





array([[6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0],
       [6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1],
       [6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0],
       [6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1],
       [6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0],
       [6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1]])



In [507]:

    
tile  = tileLeft.tolist()
q = (6,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,)
print (len(q))
# print q in tileL
res = filter(lambda x:tuple(x)==q,tile)
print res









    



17
[[6, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1]]



In [525]:

    
# [ x for x in res if sum( for y in x)]

# res[6]
# []



In [ ]:

    
curr = pre2curr



In [528]:

    
# [x for x in out









    Out[528]:





[[0, 608, 321, 112],
 [0, 608, 321, 113],
 [0, 608, 321, 114],
 [0, 608, 321, 115],
 [0, 608, 322, 116],
 [0, 162, 117],
 [0, 607, 123],
 [0, 607, 124],
 [0, 607, 125],
 [0, 607, 126],
 [0, 610, 127],
 [0, 614, 128],
 [0, 2065, 129],
 [0, 2068, 130],
 [0, 2062, 131],
 [0, 2591, 132],
 [0, 2591, 133],
 [0, 2591, 134],
 [0, 2591, 135],
 [0, 2594, 136],
 [0, 2598, 137],
 [0, 3934, 138],
 [0, 3934, 139],
 [0, 3934, 140],
 [0, 3937, 141],
 [0, 3941, 142],
 [0, 5679, 143],
 [0, 5679, 144],
 [0, 5679, 145],
 [0, 5679, 146],
 [0, 5682, 147],
 [0, 159],
 [0, 160],
 [0, 161],
 [0, 162],
 [0, 162, 117, 163],
 [0, 162, 117, 164],
 [0, 162, 117, 165],
 [0, 162, 117, 166],
 [0, 162, 117, 167],
 [0, 162, 117, 168],
 [0, 162, 117, 169],
 [0, 162, 117, 170],
 [0, 607, 124, 175],
 [0, 607, 124, 176],
 [0, 607, 124, 177],
 [0, 607, 124, 178],
 [0, 607, 124, 179],
 [0, 607, 124, 180],
 [0, 607, 124, 181],
 [0, 607, 124, 182],
 [0, 607, 124, 183],
 [0, 607, 124, 184],
 [0, 607, 125, 185],
 [0, 607, 125, 186],
 [0, 607, 125, 187],
 [0, 607, 125, 188],
 [0, 607, 125, 189],
 [0, 607, 125, 190],
 [0, 608, 321, 203],
 [0, 608, 321, 204],
 [0, 608, 321, 205],
 [0, 608, 321, 206],
 [0, 608, 321, 207],
 [0, 608, 321, 208],
 [0, 608, 321, 209],
 [0, 608, 321, 210],
 [0, 608, 321, 211]]



In [493]:

    
# tileRight.shape
# import pymi
from pymisca.util import *
def printmat(mat,sep=','):
    if isinstance(mat,np.ndarray):
        mat=  mat.tolist()
    printlines([sep.join(str(y) for y in x) for x in mat])
printmat(tile0Right)
# print mat2str(tileRight)









    



6,0,0,0,0,0,1,1,0,1,1,0,1,1,0,1,1
6,0,0,0,1,0,1,1,0,1,1,0,1,1,0,1,1
6,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1
6,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1
6,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,1
6,0,1,0,1,0,1,1,0,1,1,0,1,1,0,1,1
6,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1
6,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,1



In [508]:

    
tile  = tileRight.tolist()
# q = (6,2,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1)
q = '60110110111011011'
q = map(int,q)
q = tuple(q)
print q
print len(q)
# print q
# print q in tileRight
res = filter(lambda x:tuple(x)==q,tile)
# cu = pre2curr(tileRight)
# print np.array(res)
print res









    



(6, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1)
17
[[6, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1]]



In [346]:

    
res









    Out[346]:





[[[],
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  []],
 [[],
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  []],
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In [329]:

    
curr = map(tuple,curr)



In [331]:

    
??show_cycle



In [333]:

    
ck = res[0]
ini = np.reshape([curr[x] for x in ck],(1,-1,1))
# show_cycle(res[0],curr)









    



[[[(0, 1, 1)]
  [(0,)]
  [(0, 1, 1)]]]



In [344]:

    
# ?g.get_all_shortest_paths
res = g.get_shortest_paths(tLidx[2],tRidx)
print res









    



[[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], []]






    



/home/shouldsee/.local/lib/python2.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: Couldn't reach some vertices at structural_properties.c:740



In [257]:

    
### Look for a period 2 glider, drift 1/per on a period 2 backgd
### common product is 6
# tileG  + tileLeft



In [183]:

    
# def merge(tile0,tile1,right=1):
#     #### tile0 always on the left
# #     if not right:
# #         tmp = tile1[:]
# #         tile1 = tile0
# #         tile0 = tmp
#     if right:
#         if isinstance(tile1[0],dict):
#             tile1 = tile_flatten(tile1)
#         amat =  tile2adj(tile0,tile1,overlap=len(tile1[0])-2)
#     return amat
# amat = merge(tile0,[[None,None]+tail])
# idx=  np.where(amat)[0]

# res.sum()



In [125]:

    
%%time
Tb = 6
per = 2
dft = Tb/per
print dft
print query
print len(query)
print 2*Tb
# bkdper = Tb / Tbk
query = iter_head(itertools.cycle(bkd[::-1]),Tb)[::-1] + list(bkd) + iter_head(itertools.cycle(bkd),dft)
tile0 = main(glider=bkd,T=2*3,per=0)
tile_ref = [[None,None,] + query] 
amat = tile2adj(tile_ref,tile0,overlap=len(query))
idx =  np.where(amat)[0].ravel()
tile = [tile0[x] for x in idx]
excitable = tile
f = map(tile_flatten,tile)
print np.array(f)


query = iter_head(itertools.cycle(bkd),Tb+len(bkd))
tile_ref = [[None,None,] + query] 
amat = tile2adj(tile0,tile_ref,overlap=len(query))
idx =  np.where(amat)[0].ravel()
print idx
tile = [tile0[x] for x in idx]
refractable = tile
f = map(tile_flatten,tile)
print np.array(f)
# tile1









    



3
[0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1]
12
12
[[6 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0]
 [6 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1]
 [6 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0]
 [6 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1]
 [6 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0]
 [6 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1]
 [6 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 0]
 [6 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1]]
[  23   67  111  155  199  243  287  331  375  419  463  507  551  595
  639  683  727  771  815  859  903  947  991 1035 1079 1123 1167 1211
 1255 1299 1343 1387 1431 1475 1519 1563 1607 1651 1695 1739 1783 1827
 1871 1915 1959 2003 2047 2091 2135 2179 2223 2267 2311 2355 2399 2443
 2487 2531 2575 2619 2663 2707 2751 2795]
[[6 0 0 ... 0 1 1]
 [6 0 0 ... 0 1 1]
 [6 0 0 ... 0 1 1]
 ...
 [6 0 1 ... 0 1 1]
 [6 0 1 ... 0 1 1]
 [6 0 1 ... 0 1 1]]
CPU times: user 220 ms, sys: 0 ns, total: 220 ms
Wall time: 215 ms



In [705]:

    
# n = 1

from simpleCycles import simple_cycles
def adj2dct(adj):
    idx = np.where(adj)
    g = {x:[] for x in range(len(adj))}
    for I,O in np.transpose(idx):
        g[I] = g.get(I,[]) + [O]
    return g


def tile_flatten(x):
    def f(x):
        return (x['parity']['T'],x['parity']['per'],) + tuple(x['seq'])
    if isinstance(x,list):
        return map(f,x)
    else:
        return f(x)
#     tiles = [ (x['parity']['T'],x['partiy']['per'],) + tuple(x['seq']) for x in tdct]
#     return tiles
def par2tiles(T,per,n=1,flat=0):
#     T = 3
#     per =  2
    lst = [base2bin(str(x),10,n) for x in range(2**n)]
#     res = map(lambda x:main(x,per=per,T=T),lst);
    tiles = map(lambda x:main(x,per=per,T=T),lst);
    # tiles = np.vstack([x[T] for x in res])
    tiles = sum(tiles,[])
#     tiles = [ {'parity':{'T':T,'per':per},
#        'seq':tuple(x),} for x in np.squeeze(np.vstack(x[T] for x in res)).tolist()]
    if flat:
        tiles = map(tile_flatten,tiles)
#     tiles = [ (T,per,) + tuple(x) for x in np.squeeze(np.vstack(x[T] for x in res)).tolist()]
    return tiles 
# tile0 = par2tiles(2,0)


def safe_divide(T,per):
    if per:
        return T/per
    else:
        return 0


def isCompatible(left,right,T = 1,n =  1):
#     lPar =left.get('parity')
#     rPar =right.get('parity')    
    
    #### Currently assuming the T are the same    
    
    ##### Assuming both are of per 0
    #### Tail of left matches Head of right
#     tail = left['seq'][-2*lPar['T']:]
#     head = right['seq'][:2*rPar['T']]
    lper = left[1] 
    rper = right[1]
    ldri = safe_divide(T,lper)
    rdri = safe_divide(T,rper)
    jumplen = ldri - rdri
    assert 2*T-jumplen>=0,'Negative overlap due to huge jump'
        
#     tail = left [-(2*T-jumplen)  :     ]     ### len = 2*T - jumplen
#     head = right[2  : 2 + (2*T- jumplen)] ### len = 2*T - jummplen
    tail = left [2+n:   ]     ### len = 2*T - n
    head = right[2  : -n]        ### len = 2*T - n
    tailtail = tail[jumplen:]
    headhead = head[:-jumplen] if jumplen>0 else head
    if all(x==y for x,y in zip(headhead,tailtail)):
        consent =  headhead
        if  jumplen>0:
            jumphist = np.hstack([tail[:jumplen],head])
#             jumphist = tuple(tail[:jumplen]) + tuple(head)
            end = sample(env, ini =np.reshape(jumphist,(1,-1,1)),T=T)[-1]
            end = end.ravel()[T:-T]
            print jumphist,end
            return 0.5
        else:
    #         print head,tail
            return True
    else:
        return False

def tile2adj(tleft,tright=None,sep=0,overlap=None):
    if isinstance(tleft[0],dict):
        tleft = map(tile_flatten,tleft)
    if tright is None:
        tright = tleft        
    elif isinstance(tright[0],dict):
        tright = map(tile_flatten,tright)

    if overlap is None:
        T = tleft[0][0]
        overlap = 2*T - sep
    tleft = np.array(tleft)[:,2:]
    tright = np.array(tright)[:,2:]
    #### construct DAG from tiles
    heads = tright[:,:(overlap)]
    tails = tleft[:,-(overlap):]
#     mids  = tiles[:,T:-T]
    ##### tail of the left is the head of the right
    ##### axis= 0 is left, axis=1 is right
    adj = tails[:,None] == heads[None,:]
    adj = np.all(adj,axis=2).squeeze()
    return adj

N = 1000
def iter_head(cks,N):
    i = 0
    lst = []
    for x in cks:
        i+=1
        lst+=[x]
        if i==N:
            break
    return lst
def pre2curr(pre,mid=0):
    if isinstance(pre[0],dict):
        pre = map(tile_flatten,pre)
    out = []    
    for x in pre:
#         T = x[]
        T,per = x[:2]
        move = 0 if (per==0) | mid else  cmp(per,0)*(T//abs(per))
        out.append(x[2+T+move:-T+move])
    return out
#     print pre[:5]
# pre2curr(tile0)
def show_cycle(ck,curr,callback = np.transpose,**kwargs):
#     print ck
    ini = np.reshape([curr[x] for x in ck],(1,-1,1))
    out = sample(env,ini=ini,**kwargs)
    print np.shape(out)
    showsptime(callback(out.squeeze()))
    plt.show()

    
import scipy.spatial.distance as spdist
# spdist.pdist(np.array(tile0),isCompatible)
# ?spdist.cdist
def f1():
#     X = np.array(tile0)
    X = map(tile_flatten,tile0)
    D = spdist.cdist(X,X,isCompatible)
    print D.shape
    return D


tile0 = par2tiles(3,0)
tile1 = par2tiles(3,3)

%time D1 = f1()
plt.imshow(D1)
plt.show()

%time D2 = tile2adj(map(tile_flatten,tile0))
plt.imshow(D2)
plt.show()
assert np.all(D1==D2),'Result disagree'

# def f2():
# #     X = np.array(tile0)
# #     X = tile0
#     D = spdist.cdist(tile1,tile0,isCompatible)
#     print D.shape
#     return D
# print len(tile0[0])
# %time f2()
# {x['seq'] for x in tile1} - {x['seq'] for x in tile0}
# tile1









    



(97, 97)
CPU times: user 60 ms, sys: 0 ns, total: 60 ms
Wall time: 59.3 ms






    












    



CPU times: user 0 ns, sys: 0 ns, total: 0 ns
Wall time: 732 µs



In [833]:

    
D = tile2adj(tile1)









    Out[833]:





array([[ True, False, False, ..., False, False, False],
       [False, False, False, ..., False, False, False],
       [False, False, False, ..., False, False, False],
       ...,
       [False, False, False, ..., False, False, False],
       [False, False, False, ..., False, False, False],
       [False, False, False, ...,  True,  True, False]])



In [842]:

    
tile = tile1 + tile0
D = tile2adj(tile)
curr = pre2curr(tile)

cks = simple_cycles(adj2dct(D))
cks = iter_head(cks,1000)
# cks = list(cks)
# print len(cks)

# print cks_ptn.shape



In [841]:



In [ ]:

    
tile



In [850]:

    
seqs = [ [curr[x] for x in ck] for ck in cks]
dft_local  =[ tuple(tile[x]['parity']['per'] for x in ck) for ck in cks] 
dft_gb = [sum(x) for x in dft_local]



In [861]:

    
# showsptime(sample(env,ini=seqs[0]))
# print 
i = 0
print dft_local[i]
show_cycle(cks[i],curr,callback=identity,T=20)









    



(0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 3, 3, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 3, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 3, 0, 3, 0, 0, 0, 0, 3, 0)
(21, 1, 56, 1)



In [859]:



In [688]:

    
%%time
### Get the list of valid tiles
n = 1
T = 3
per =  2
lst = [base2bin(str(x),10,n) for x in range(2**n)]
res = map(lambda x:main(x,per=per,T=T),lst);
tiles = np.vstack([x[T] for x in res])
print 'Tiles shape:',tiles.shape


#### construct DAG from tiles
heads = tiles[:,:2*T]
tails = tiles[:,-2*T:]
mids  = tiles[:,T:-T]
##### tail of the left is the head of the right
##### axis= 0 is left, axis=1 is right
adj = tails[:,None] == heads[None,:]
print adj.shape
adj = np.all(adj,axis=2).squeeze()
print adj.shape
# print adj.shape
plt.imshow(adj[:,:])
# plt.imshow()
plt.show()
idx = np.where(np.diag(adj))[0]
# print tails.shape

G = adj2dct(adj)
cks = list(simple_cycles(G))
print len(cks)
print cks[0]









    



Tiles shape: (57, 7, 1)
(57, 57, 6, 1)
(57, 57)






    












    



1
[0]
CPU times: user 196 ms, sys: 144 ms, total: 340 ms
Wall time: 166 ms



In [667]:

    
TILES = {tuple(np.ravel(mids[x]).tolist()) for x in cks}
# set(TILES)



In [622]:

    
cks = simple_cycles(G)
lst = []

i = 0
for x in cks:
#     print x
    lst += [x]
    i+=1
    if i==100:
        break
cks = lst



In [513]:



In [648]:

    
G = adj2dct(adj)
cks = list(simple_cycles(G))
print len(cks)

# mids[cks[0]]
print 'T=',T
# print cks
ck = cks[0]
print ck
print np.hstack([heads[ck[1:]],tails[ck][:-1]]).squeeze()
print tiles[ck].squeeze()
print mids[ck].squeeze()









    



47260
T= 3
[2, 50, 55, 23, 89, 84, 71, 95, 93, 45, 87, 78, 19, 37, 73, 10, 64, 83, 70, 92, 44, 86, 32, 63, 79, 20, 85, 28, 12, 26, 51, 58, 69, 91, 42, 36, 72, 4, 11, 24]
[[0 0 0 1 1 0 0 0 0 1 1 0]
 [0 0 1 1 0 1 0 0 1 1 0 1]
 [0 1 1 0 1 1 0 1 1 0 1 1]
 [1 1 0 1 1 1 1 1 0 1 1 1]
 [1 0 1 1 1 1 1 0 1 1 1 1]
 [0 1 1 1 1 1 0 1 1 1 1 1]
 [1 1 1 1 1 0 1 1 1 1 1 0]
 [1 1 1 1 0 1 1 1 1 1 0 1]
 [1 1 1 0 1 1 1 1 1 0 1 1]
 [1 1 0 1 1 0 1 1 0 1 1 0]
 [1 0 1 1 0 0 1 0 1 1 0 0]
 [0 1 1 0 0 1 0 1 1 0 0 1]
 [1 1 0 0 1 0 1 1 0 0 1 0]
 [1 0 0 1 0 1 1 0 0 1 0 1]
 [0 0 1 0 1 1 0 0 1 0 1 1]
 [0 1 0 1 1 1 0 1 0 1 1 1]
 [1 0 1 1 1 1 1 0 1 1 1 1]
 [0 1 1 1 1 0 0 1 1 1 1 0]
 [1 1 1 1 0 1 1 1 1 1 0 1]
 [1 1 1 0 1 0 1 1 1 0 1 0]
 [1 1 0 1 0 1 1 1 0 1 0 1]
 [1 0 1 0 1 1 1 0 1 0 1 1]
 [0 1 0 1 1 0 0 1 0 1 1 0]
 [1 0 1 1 0 1 1 0 1 1 0 1]
 [0 1 1 0 1 0 0 1 1 0 1 0]
 [1 1 0 1 0 0 1 1 0 1 0 0]
 [1 0 1 0 0 0 1 0 1 0 0 0]
 [0 1 0 0 0 1 0 1 0 0 0 1]
 [1 0 0 0 1 1 1 0 0 0 1 1]
 [0 0 0 1 1 1 0 0 0 1 1 1]
 [0 0 1 1 1 1 0 0 1 1 1 1]
 [0 1 1 1 1 0 0 1 1 1 1 0]
 [1 1 1 1 0 0 1 1 1 1 0 0]
 [1 1 1 0 0 1 1 1 1 0 0 1]
 [1 1 0 0 1 0 1 1 0 0 1 0]
 [1 0 0 1 0 0 1 0 0 1 0 0]
 [0 0 1 0 0 0 0 0 1 0 0 0]
 [0 1 0 0 0 0 0 1 0 0 0 0]
 [1 0 0 0 0 1 1 0 0 0 0 1]]
[[0 0 0 0 1 1 0]
 [0 0 0 1 1 0 1]
 [0 0 1 1 0 1 1]
 [0 1 1 0 1 1 1]
 [1 1 0 1 1 1 1]
 [1 0 1 1 1 1 1]
 [0 1 1 1 1 1 0]
 [1 1 1 1 1 0 1]
 [1 1 1 1 0 1 1]
 [1 1 1 0 1 1 0]
 [1 1 0 1 1 0 0]
 [1 0 1 1 0 0 1]
 [0 1 1 0 0 1 0]
 [1 1 0 0 1 0 1]
 [1 0 0 1 0 1 1]
 [0 0 1 0 1 1 1]
 [0 1 0 1 1 1 1]
 [1 0 1 1 1 1 0]
 [0 1 1 1 1 0 1]
 [1 1 1 1 0 1 0]
 [1 1 1 0 1 0 1]
 [1 1 0 1 0 1 1]
 [1 0 1 0 1 1 0]
 [0 1 0 1 1 0 1]
 [1 0 1 1 0 1 0]
 [0 1 1 0 1 0 0]
 [1 1 0 1 0 0 0]
 [1 0 1 0 0 0 1]
 [0 1 0 0 0 1 1]
 [1 0 0 0 1 1 1]
 [0 0 0 1 1 1 1]
 [0 0 1 1 1 1 0]
 [0 1 1 1 1 0 0]
 [1 1 1 1 0 0 1]
 [1 1 1 0 0 1 0]
 [1 1 0 0 1 0 0]
 [1 0 0 1 0 0 0]
 [0 0 1 0 0 0 0]
 [0 1 0 0 0 0 1]
 [1 0 0 0 0 1 1]]
[0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1
 0 0 0]



In [684]:

    
ck = cks[20]
print ck
ini = np.reshape(mids[ck],(1,-1,1))
out = sample(env,ini=ini)
print np.shape(out)
showsptime(out.squeeze().T)
plt.show()









    



[2, 50, 55, 23, 89, 84, 71, 95, 93, 45, 87, 78, 19, 37, 73, 10, 64, 83, 70, 92, 43, 85, 28, 12, 26, 51, 58, 69, 90, 41, 35, 25, 49, 52, 17, 34, 24]
(101, 1, 37, 1)



In [400]:

    
def markov(tmat):    
    if not np.all(np.sum(tmat,axis=1)==1):
        print "[WARN] transition matrix is not normalised"
#         tmat = 

tmat = adj/np.sum(adj,axis=1,keepdims=1)
markov(tmat)    



# def tile()
# ?np.tile









    



[WARN] transition matrix is not normalised






    



/home/shouldsee/.local/lib/python2.7/site-packages/ipykernel_launcher.py:5: RuntimeWarning: divide by zero encountered in divide
  """



In [394]:

    
print mids[idx].squeeze()









    



[[0 0 0 0 0]
 [0 1 1 0 1]
 [1 0 1 1 0]
 [1 0 0 1 1]
 [1 1 0 1 1]]



In [355]:

    
n = 5
lst = [base2bin(str(x),10,n) for x in range(2**n)]
res[2]









    Out[355]:





[array([[[0],
         [0],
         [0],
         [1],
         [0]]]),
 array([], shape=(0, 7, 1), dtype=int64),
 array([], shape=(0, 9, 1), dtype=int64),
 array([], shape=(0, 11, 1), dtype=int64)]



In [299]:

    
out = np.array(outlst[2])
print out.shape









    



(12, 9, 1)



In [306]:

    
env.alias









    Out[306]:





'118'



In [330]:

    
# showsptime(np.array(outlst[2]))
outlst =main('01000',per=0)
out = np.array(outlst[3])
showsptime(np.squeeze(out).T)
plt.show()



In [320]:

    
# showsptime(np.array(outlst[2]))
outlst =main('01110',per=2)
out = np.array(outlst[4])
showsptime(np.squeeze(out).T)
plt.show()



In [316]:

    
out = np.array(outlst[4])
showsptime(np.squeeze(out).T)
plt.show()



In [243]:

    
showsptime(out.T)
plt.show()



In [246]:

    
showsptime(out.T)
plt.show()



In [234]:

    
bin(51)









    Out[234]:





'0b110011'



In [224]:

    
int(glider[::-1],2)









    Out[224]:





99



In [208]:

    
ini_int.ravel()
# [ini.size//2]









    Out[208]:





array([60, 57, 51, 39, 15, 30])



In [226]:

    
# ini.size
# ini_int[2]
ini_int.flat[(ini.size-1)//2]









    Out[226]:





99



In [229]:

    
fir = np.reshape(2**np.arange(ini.size),(1,-1,1))
ini_int = convolve_int(ini,fir,'reflect').flat[(ini.size-1)//2]
recur = convolve_int(parent[paridx.ravel()],fir,'wrap') == ini_int









    Out[229]:





0.00569155446756426



In [184]:

    
parent.shape









    Out[184]:





(262144, 18, 1)



In [183]:



In [175]:

    
ini.shape









    Out[175]:





(1, 4, 1)



In [96]:

    
# import functools
# functools.partial(env.adv,method='valid')









    Out[96]:





<functools.partial at 0x7fbae06cbec0>



In [5]:

    
??CA_sys