AT_abc442_b [ABC442B] Music Player

Takahashi has a music player. Initially, the volume is $ 0 $ and the music is stopped. From now on, $ Q $ operations will be performed in order. The $ i $ -th operation is represented by an integer $ A_i $ , which means the following: - If $ A_i = 1 $ , increase the volume by $ 1 $ . - If $ A_i = 2 $ , if the current volume is $ 1 $ or more, decrease it by $ 1 $ ; if it is $ 0 $ , do nothing. - If $ A_i = 3 $ , if the music is stopped, play it; if the music is playing, stop it. For $ i = 1, 2, \ldots, Q $ , solve the following problem: - Determine whether the music is playing at volume $ 3 $ or more immediately after the $ i $ -th operation.

The input is given from Standard Input in the following format: > $ Q $ > > $ A_1 $ > > $ A_2 $ > > $ \vdots $ > > $ A_Q $

Output $ Q $ lines. The $ i $ -th line should contain `Yes` if the music is playing at volume $ 3 $ or more immediately after the $ i $ -th operation, and `No` otherwise.

### Sample Explanation 1 - After the $ 1 $ -st operation, the volume is $ 0 $ and the music is stopped. - After the $ 2 $ -nd operation, the volume is $ 1 $ and the music is stopped. - After the $ 3 $ -rd operation, the volume is $ 1 $ and the music is playing. - After the $ 4 $ -th operation, the volume is $ 2 $ and the music is playing. - After the $ 5 $ -th operation, the volume is $ 2 $ and the music is stopped. - After the $ 6 $ -th operation, the volume is $ 3 $ and the music is stopped. - After the $ 7 $ -th operation, the volume is $ 4 $ and the music is stopped. - After the $ 8 $ -th operation, the volume is $ 4 $ and the music is playing. - After the $ 9 $ -th operation, the volume is $ 3 $ and the music is playing. - After the $ 10 $ -th operation, the volume is $ 2 $ and the music is playing. ### Constraints - $ 1 \leq Q \leq 2 \times 10^5 $ - $ A_i \in \lbrace 1, 2, 3 \rbrace $ - All input values are integers.