NAME_1 and NAME_2 just became friends with NAME_3, and they want to know when her birthday is.

NAME_3 gives them a list of 10 possible dates:

May 15, May 16, May 19
June 17, June 18
July 14, July 16
August 14, August 15, August 17
NAME_3 then tells NAME_1 and NAME_2 separately the month and the day of her birthday respectively.

NAME_1: I don’t know when NAME_3’s birthday is, but I know that NAME_2 doesn’t know too.

NAME_2: At first I don’t know when NAME_3’s birthday is, but I know now.

NAME_1: Then I also know when NAME_3’s birthday is.

So when is NAME_3’s birthday? In your entire response, the letter g should appear at most once.
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