Find the LCA

You are given an integer sequence $A\_1,A\_2,\ldots,A\_N$. You'll make a rooted tree with $N$ vertices numbered from $1$ through $N$. The vertex $1$ is the root, and for each vertex $i$ ($2 \leq i \leq N$), its parent $p\_i$ must satisfy $p\_i\<i$.

You define the score of a rooted tree as follows:

• Let $x$ be the lowest common ancestor of the vertex $N-1$ and the vertex $N$. Then, the score is $\prod\_{v \in (\text{subtree rooted at $x$})} A\_v$ Note that we consider $x$ itself is in the subtree rooted at $x$. 

There are $(N-1)!$ ways to make a tree. Find the sum of scores of all possible trees, modulo $998244353$.

The first line contains an integer $N$ ($3 \leq N \leq 250000$).

The second line contains integers $A\_1,A\_2,\ldots,A\_N$ ($1 \leq A\_i < 998244353$).

Print the answer.