We know that Daizhenyang is chasing a girlfriend. As we all know, whenever you chase a beautiful girl, there'll always be an opponent, or a rival. In order to take one step ahead in this chasing process, Daizhenyang decided to prove to the girl that he's better and more intelligent than any other chaser. So he arranged a simple game: Coin Flip Game. He invited the girl to be the judge.
In this game, n coins are set in a row, where n is smaller than 10^8. They took turns to flip coins, to flip one coin from head-up to tail-up or the other way around. Each turn, one can choose 1, 2 or 3 coins to flip, but the rightmost selected must be head-up before flipping operation. If one cannot make such a flip, he lost.
As we all know, Daizhenyang is a very smart guy (He's famous for his 26 problems and Graph Theory Unified Theory-Network Flow does it all ). So he will always choose the optimal strategy to win the game. And it's a very very bad news for all the competitors.
But the girl did not want to see that happen so easily, because she's not sure about her feelings towards him. So she wants to make Daizhenyang lose this game. She knows Daizhenyang will be the first to play the game. Your task is to help her determine whether her arrangement is a losable situation for Daizhenyang.
For simplicity, you are only told the position of head-up coins. And due to the girl's complicated emotions, the same coin may be described twice or more times. The other coins are tail-up, of course.
Coins are numbered from left to right, beginning with 0.