CF1952E Sweep Line

Be careful not to make a mistake. You might have to start all over again. — Someone, probably

The first line contains one integer $ n $ ( $ 1 \leq n \leq 10^5 $ ) — the length of the array $ a $ . The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 0 \leq a_i \leq 2 $ ) — the array $ a $ .

Output a single integer — the number of solutions, modulo $ 20240401 $ .

In the first sample, the array looks like this: $ \color{blue}{1} $ $ \color{blue}{1} $ $ \color{darkgreen}{2} $ $ \color{blue}{1} $ $ \color{blue}{1} $ $ \color{darkgreen}{2} $ $ \color{gray}{0} $ Obviously, the answer here is $ 1 \pmod{20240401} $ . In the second sample, the array looks like this: $ \color{blue}{1} $ $ \color{blue}{1} $ $ \color{darkgreen}{2} $ $ \color{blue}{1} $ $ \color{blue}{1} $ $ \color{blue}{1} $ $ \color{gray}{0} $ I do not know why the answer here is $ 2 \pmod{20240401} $ , I had to take a guess. In the third sample, the array looks like this: $ \color{gray}{0} $ $ \color{blue}{1} $ $ \color{darkgreen}{2} $ $ \color{blue}{1} $ $ \color{blue}{1} $ $ \color{blue}{1} $ $ \color{gray}{0} $ If the answer here is not $ 0 \pmod{20240401} $ , I am literally going to explode.