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#! /usr/bin/python3
import math
def is_rare(t: str):
d=t[::-1]
dn=int(d)
tn=int(t)
if dn >= tn:
return 0
for cn in [tn+dn,tn-dn]:
cm=cn % 10
if cm==2 or cm==3 or cm==7 or cm==8:
return 0
s=int(math.sqrt(cn))
if s*s != cn:
return 0
return 1
def rn(d):
out=list()
mxm=10**(d-2)-1
for a in [2,4,6,8]:
for q in [0,2,3,5,7,8]:
if a==2 and q!=2:
continue
if a==4 and q!=0:
continue
if a==6 and q!=0 and q!=5:
continue
if a==8 and q!=2 and q!=3 and q!=7 and q!=8:
continue
if d==2:
ts=str(a) + str(q)
if is_rare(ts):
out.append(int(ts))
else:
for md in range(mxm+1):
mds=("{:0"+str(d-2)+"d}").format(md)
b=int(mds[0])
p=int(mds[len(mds)-1])
if a==2 and b!=p:
continue
if a==4 and abs(b-p)%2 != 0:
continue
if a==6 and abs(b-p)%2 != 1:
continue
if a==8:
if q==2 and b+p != 9:
continue
if q==3 and b-p != 7 and p-b != 3:
continue
if q==7 and b+p != 1 and b+p != 11:
continue
if q==8 and b!=p:
continue
ts=str(a)+mds+str(q)
if is_rare(ts):
out.append(int(ts))
return out
import unittest
class TestRn(unittest.TestCase):
def test_ex1(self):
self.assertEqual(rn(2),[65],'example 1')
def test_ex2(self):
self.assertEqual(rn(6),[621770],'example 2')
def test_ex3(self):
self.assertEqual(rn(9),[281089082],'example 3')
unittest.main()
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