Takahashi has various colors of socks in his chest of drawers. The colors of the socks are represented by integers from $1$ to $N$, and there are $A_i\ (\geq 2)$ socks of color $i$.

He is about to choose which socks to wear today by performing the following operation:

-   Continue to randomly draw one sock at a time from the chest, with equal probability, until he can make a pair of socks of the same color from those he has already drawn. Once a sock is drawn, it will not be returned to the chest.

Find the expected value, modulo $998244353$, of the number of times he has to draw a sock from the chest.

What does it mean to find the expected value modulo $998244353$? It can be proved that the sought expected value is always rational. Furthermore, the constraints of this problem guarantee that if the expected value is expressed as an irreducible fraction $\frac{y}{x}$, then $x$ is not divisible by $998244353$. Here, there exists a unique integer $z$ between $0$ and $998244352$, inclusive, such that $xz \equiv y \pmod{998244353}$. Find this $z$.

The input is given from Standard Input in the following format:

```
$N$
$A_1$ $A_2$ $\dots$ $A_N$
```

Print the answer.

-   $1\leq N \leq 3\times 10^5$
-   $2\leq A_i \leq 3000$
-   All input values are integers.

665496238

For example, the operation could be performed as follows:

1. Draw a sock of color 1 from the chest. There remains one sock of color 1 and two socks of color 2 in the chest.
2. Draw a sock of color 2 from the chest. There remains one sock each of colors 1 and 2 in the chest.
3. Draw a sock of color 1 from the chest. The socks drawn so far are two of color 1 and one of color 2, allowing a pair of color 1 socks to be made, thus ending the operation.

In this example, Takahashi draws a sock from the chest three times.
The expected number of times Takahashi draws a sock from the chest is 3 with probability $\frac{2}{3}$ and 2 with probability $\frac{1}{3}$, so the expected value is $3\times \frac{2}{3}+2×\frac{1}{3}=\frac{8}{3}≡665496238\ (\bmod\ {998244353})$.