Faineant Komorebi comes to play games with Setsuna again! To make the game fun, Komorebi decides to ask Setsuna to create a new game that he has never played before.

Thus, Setsuna gives the rule of the game as follow:

1. Setsuna brings a pile of stones and chooses a magical number , where .
2. Komorebi brings a pile of stones, where . So now there are two piles of stones, each containing stones and stones.
3. Setsuna and Komorebi take turns to take the stones, and Setsuna goes first. If someone can't do any operation in this turn, he loses the game.

During each turn, the player has only two choices:

1. Take stones from one of the piles, where .
2. Take stones from Setsuna's pile and stone from Komorebi's pile, where .

Even if Komorebi's brain is exhausted, he still thinks there must be something wrong with the game. When Setsuna gives the number of stones in the first pile, how many stones should Komorebi bring in order to be sure to win?

As Komorebi is quite lazy, if there are multiple answers, output the minimum one.

Formally, when and are determined, find the minimum to ensure that Komorebi wins.