def brute(n):
r=1
for x in xrange(3<<(n-2),1<<n):
c=1
y=x
while 1:
y=((y&1)<<(n-1))|(y>>1)
if bin(x^y).count('1')!=n/2:
break
c+=1
if c>r:
r=c
X=x
return r,bin(X)[2:]
for n in xrange(4,30,4):
print n,brute(n)
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