CF1286D.LCC

An infinitely long Line Chillland Collider (LCC) was built in Chillland. There are $n$ pipes with coordinates $x_i$ that are connected to LCC. When the experiment starts at time 0, $i$-th proton flies from the $i$-th pipe with speed $v_i$. It flies to the right with probability $p_i$ and flies to the left with probability $(1 - p_i)$. The duration of the experiment is determined as the time of the first collision of any two protons. In case there is no collision, the duration of the experiment is considered to be zero.

Find the expected value of the duration of the experiment.

Illustration for the first example

在 Chillland 建造了一台无限长的直线 Chillland 对撞机（LCC）。有 $n$ 根管道，其坐标为 $x_i$，连接至 LCC。实验于时刻 0 启动，第 $i$ 个质子从第 $i$ 根管道出发，速度为 $v_i$。该质子以概率 $p_i$ 向右运动，以概率 $(1 - p_i)$ 向左运动。实验持续时间定义为任意两个质子首次发生碰撞的时刻；若不会发生任何碰撞，则实验持续时间视为 0。

求实验持续时间的期望值。

第一个样例的示意图

The first line of input contains one integer $n$ — the number of pipes ($1 \le n \le 10^5$). Each of the following $n$ lines contains three integers $x_i$, $v_i$, $p_i$ — the coordinate of the $i$-th pipe, the speed of the $i$-th proton and the probability that the $i$-th proton flies to the right in percentage points ($-10^9 \le x_i \le 10^9, 1 \le v \le 10^6, 0 \le p_i \le 100$). It is guaranteed that all $x_i$ are distinct and sorted in increasing order.

输入的第一行包含一个整数 $n$ —— 管道的数量（$1 \le n \le 10^5$）。接下来的 $n$ 行中，每行包含三个整数 $x_i$、$v_i$、$p_i$ —— 分别表示第 $i$ 条管道的坐标、第 $i$ 个质子的速度，以及第 $i$ 个质子向右飞行的概率（以百分比数值表示）（$-10^9 \le x_i \le 10^9$，$1 \le v_i \le 10^6$，$0 \le p_i \le 100$）。保证所有 $x_i$ 互不相同且按升序排列。

It's possible to prove that the answer can always be represented as a fraction $P/Q$, where $P$ is an integer and $Q$ is a natural number not divisible by $998\,244\,353$. In this case, print $P \cdot Q^{-1}$ modulo $998\,244\,353$.

可以证明答案总能表示为分数 $P/Q$，其中 $P$ 是整数，$Q$ 是不被 $998\,244\,353$ 整除的正整数。此时，请输出 $P \cdot Q^{-1}$ 对 $998\,244\,353$ 取模的结果。