There are $N$ cards called card $1$, card $2$, $\ldots$, card $N$. On card $i$ $(1\leq i\leq N)$, an integer $A_i$ is written. For $K=1, 2, \ldots, N$, solve the following problem. > We have a bag that contains $K$ cards: card $1$, card $2$, $\ldots$, card $K$. > Let us perform the following operation twice, and let $x$ and $y$ be the numbers recorded, in the recorded order. > > > Draw a card from the bag uniformly at random, and record the number written on that card. Then, **return the card to the bag**. > > Print the expected value of $\max(x,y)$, modulo $998244353$ (see Notes). > Here, $\max(x,y)$ denotes the value of the greater of $x$ and $y$ (or $x$ if they are equal). #### Notes It can be proved that the sought expected value is always finite and rational. Additionally, under the Constraints of this problem, when that value is represented as $\frac{P}{Q}$ with two coprime integers $P$ and $Q$, it can be proved that there is a unique integer $R$ such that $R \times Q \equiv P\pmod{998244353}$ and $0 \leq R \lt 998244353$. Print this $R$.

The input is given from Standard Input in the following format: >$N$\ >$A_1$ $A_2$ $\ldots$ $A_N$ #### Constraints - $1 \leq N \leq 2\times 10^5$ - $1 \leq A_i \leq 2\times 10^5$ - All values in the input are integers.

Print $N$ lines. The $i$\-th line $(1\leq i\leq N)$ should contain the answer to the problem for $K=i$.

***For Sample #1:*** For instance, the answer for $K=2$ is found as follows. The bag contains card $1$ and card $2$, with $A_1=5$ and $A_2=7$ written on them, respectively. - If you draw card $1$ in the first draw and card $1$ again in the second draw, we have $x=y=5$, so $\max(x,y)=5$. - If you draw card $1$ in the first draw and card $2$ in the second draw, we have $x=5$ and $y=7$, so $\max(x,y)=7$. - If you draw card $2$ in the first draw and card $1$ in the second draw, we have $x=7$ and $y=5$, so $\max(x,y)=7$. - If you draw card $2$ in the first draw and card $2$ again in the second draw, we have $x=y=7$, so $\max(x,y)=7$. These events happen with the same probability, so the sought expected value is $\frac{5+7+7+7}{4}=\frac{13}{2}$. We have $499122183\times 2\equiv 13 \pmod{998244353}$, so $499122183$ should be printed.

AtCoder [ABC276F]