aaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaabaaaaba
