1
aaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaaaaaabbbbbbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbbbbbbbbbaaaaaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaaaaaabbbbbbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaaaaaabbbbbbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaabbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaabbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbaaaabbbbbbbbbbbbaaaaaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaa
aaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaaaaaabbbbbbbbaaaabbbbaaaaaaaabbbbaaaabbbbbbbbaaaabbbbaaaaaaaabbbbbbbbaaaaaaaabbbbaaaabbbbbbbbaaaa
