CF1866M.Mighty Rock Tower

Pak Chanek comes up with an idea in the midst of boredom to play a game. The game is a rock tower game. There is a big rock that is used as a base. There are also $N$ small identical rocks that Pak Chanek will use to build a rock tower with a height of $N$ above the base rock.

Initially, there are no small rocks that are located above the base rock. In other words, the height of the tower above the base rock is initially $0$. In one move, Pak Chanek can place one small rock onto the top of the tower which makes the height of the tower above the base rock increase by $1$. Each time Pak Chanek place one small rock, the following will happen after the small rock is placed:

• Let's say $x$ is the height of the tower above the base rock right after the small rock is placed.
• There is a probability of $P_x$ percent that the topmost rock falls.
• If $x \geq 2$ and the topmost rock falls, then there is another probability of $P_x$ percent that the $2$-nd topmost rock also falls.
• If $x \geq 3$ and the $2$-nd topmost rock falls, then there is another probability of $P_x$ percent that the $3$-rd topmost rock also falls.
• If $x \geq 4$ and the $3$-rd topmost rock falls, then there is another probability of $P_x$ percent that the $4$-th topmost rock also falls.
• And so on.

If the tower successfully reaches a height of $N$ without any rocks falling after that, then the game is ended.

If given an integer array $[P_1, P_2, \ldots, P_N]$, what is the expected value of the number of moves that Pak Chanek needs to do to end the game? It can be proven that the expected value can be represented as an simple fraction $\frac{P}{Q}$ where $Q$ is coprime to $998\,244\,353$. Output the value of $P \times Q^{-1}$ modulo $998\,244\,353$.

帕克·查内克在百无聊赖之际想出了一个游戏点子。这个游戏叫做“石塔游戏”。游戏中有一块大石头，作为底座；此外还有 $N$ 块完全相同的小石头，帕克·查内克将用它们在底座之上搭建一座高度为 $N$ 的石塔。

初始时，底座上方没有任何小石头，即石塔在底座之上的高度为 $0$。每一步操作中，帕克·查内克可将一块小石头放置在石塔顶端，使石塔在底座之上的高度增加 $1$。每次放置一块小石头后，将发生如下事件：

• 设 $x$ 为该小石头刚被放置完毕后，石塔在底座之上的高度；
• 此时最顶端的石头有 $P_x$ 的概率掉落；
• 若 $x \geq 2$ 且最顶端的石头掉落，则第二顶端的石头也有 $P_x$ 的概率掉落；
• 若 $x \geq 3$ 且第二顶端的石头掉落，则第三顶端的石头也有 $P_x$ 的概率掉落；
• 若 $x \geq 4$ 且第三顶端的石头掉落，则第四顶端的石头也有 $P_x$ 的概率掉落；
• 依此类推。

若石塔成功达到高度 $N$，且此后再无任何石头掉落，则游戏结束。

现给定一个整数数组 $[P_1, P_2, \ldots, P_N]$，问：帕克·查内克结束游戏所需的操作步数的期望值是多少？可以证明该期望值可表示为最简分数 $\frac{P}{Q}$，其中 $Q$ 与 $998\,244\,353$ 互质。请输出 $P \times Q^{-1} \bmod 998\,244\,353$ 的值。

The first line contains a single integer $N$ ($1 \leq N \leq 2\cdot10^5$) — the required height of the rock tower.

The second line contains $N$ integers $P_1, P_2, P_3, \ldots, P_N$ ($0 \leq P_i \leq 99$).

第一行包含一个整数 $N$（$1 \leq N \leq 2\cdot10^5$）—— 表示岩石塔所需的高度。

第二行包含 $N$ 个整数 $P_1, P_2, P_3, \ldots, P_N$（$0 \leq P_i \leq 99$）。

An integer representing the expected value of the number of moves that Pak Chanek needs to do to end the game, modulo $998\,244\,353$.

一个整数，表示 Pak Chanek 为结束游戏所需移动次数的期望值对 $998\,244\,353$ 取模的结果。

In the first example, the expected value of the number of moves that Pak Chanek needs to do to end the game is $\frac{19}{2}$.

在第一个例子中，Pak Chanek 为结束游戏所需移动次数的期望值为 $\frac{19}{2}$。