Problem Description

After finishing her last exam, Audrey decides to relax by playing Honkai: Star Rail.

On each of the next $n$ days, she plays during an open time interval $(s,e)$. Her smartwatch checks her stress once per day. It independently chooses a real time $t_0$ uniformly at random from the open interval $(a,b)$. If $s<t_0<e$, the watch reports that Audrey is relaxed; otherwise, it reports that she is stressed. The values $a$ and $b$ are the same every day.

Compute the probability that the watch reports Audrey as stressed on at least one day.

Input Format

The first line contains three integers $n$, $a$, and $b$ ($1\le n\le20$, $1\le a<b\le50$).

Each of the next $n$ lines contains two integers $s$ and $e$ ($1\le s<e\le50$), Audrey's open playing interval on that day.

Output Format

Output the probability that Audrey is reported as stressed on at least one day. An answer is accepted if its absolute or relative error is at most $10^{-6}$.

2 19 39
18 31
28 50

0.67