2020 年 “联想杯”全国高校程序设计在线邀请赛暨第三届上海理工大学程序设计竞赛

G. Gentle Jena

… Why don’t you come to the planetarium?

The beautiful twinkling of eternity that will never fade, no matter what.

All the stars in the sky are waiting for you…

A planetarium, it was once where people went to soothe their hearts by gazing at a starry sky.

And Yumemi, a planetarium guide who has been waiting for a visitor for a long time, is looking up at the stars.

Stars in the sky can be defined by their brightness, denoted by $S=\{b_1,b_2,\cdots ,b_n\}$.

Yumemi found that stars always appear in groups, and she thinks the beauty of the starry night depends on the darkest one, so she defined the beauty value as
$$B(S)=\sum _{1\le l\le r\le |S|}f(l,r)\text{mod}998244353$$
where
$$f(l,r)=\underset{l\le i\le r}{min}\{b_i\}$$
But the night sky is not always the same. The movement of celestial bodies will make more and more stars in the night sky. The following events will happen in order every second:

1. There are exactly $i$ stars in the sky so $S=\{b_1,b_2,\cdots ,b_i\}$. A star with brightness $b_{i+1}$ appears, and it will be appended to the end of the sequence $S$, so it will be $S=\{b_1,b_2,\cdots ,b_{i+1}\}$.
2. Yumemi records the value (i.e., She calculates the value of $B(S)$).

At the beginning, there is no star in the sky, so $S=\{\}$ initially.

As time goes by, because she is not as good at calculation as before, the task will be given to you.

Note that the sequence is given in a modified way.