CF1558A Charmed by the Game

Alice 和 Borys 在打网球。 网球比赛有很多局，每局有一个人发球，有一个人接发球。这样轮流交换，一人一局。 每局比赛都有一个胜者，如果胜者是发球者，那么称为保发，反之称为破发。 我们知道 Alice 赢了 $a$ 局，Borys 赢了 $b$ 局，但我们不知道谁先发球和每局谁赢了。 问所有可能的总破发次数。

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In the first test case, any number of breaks between $ 0 $ and $ 3 $ could happen during the match: - Alice holds serve, Borys holds serve, Alice holds serve: $ 0 $ breaks; - Borys holds serve, Alice holds serve, Alice breaks serve: $ 1 $ break; - Borys breaks serve, Alice breaks serve, Alice holds serve: $ 2 $ breaks; - Alice breaks serve, Borys breaks serve, Alice breaks serve: $ 3 $ breaks. In the second test case, the players could either both hold serves ( $ 0 $ breaks) or both break serves ( $ 2 $ breaks). In the third test case, either $ 2 $ or $ 3 $ breaks could happen: - Borys holds serve, Borys breaks serve, Borys holds serve, Borys breaks serve, Borys holds serve: $ 2 $ breaks; - Borys breaks serve, Borys holds serve, Borys breaks serve, Borys holds serve, Borys breaks serve: $ 3 $ breaks.