P8774 [Lanqiao Cup 2022 NOI Qualifier A] Tree-Climbing Beetle

A beetle wants to climb a tree of height $n$. It starts at the root, at height $0$. When it tries to climb from height $i-1$ to height $i$, it falls back to the root with probability $P_{i}$. Find the expected time it takes to climb from the root to the top of the tree.

The first line contains an integer $n$, the height of the tree. The next $n$ lines each contain two integers $x_{i}, y_{i}$, separated by a space, meaning $P_{i}=\frac{x_{i}}{y_{i}}$.

Output one line containing one integer, representing the answer. The answer is a rational number; output its value modulo the prime $998244353$. For a rational number $\frac{a}{b}$, its value modulo a prime $P$ is the integer $c$ such that $0 \leq c

Constraints: For $20\%$ of the testdata, $n \leq 2$, $1 \leq x_{i}