vev is addicted to the game Avalon. She is currently playing a game and wants to make an informed decision on who to put on her quest. There are $G$ distinct groups of players, each with $p_g$ players. Of the $p_g$ players in the group, $e_g$ of them are considered to be evil $(e_g\le p_g)$. Assuming vev chooses a single player randomly from each group, what is the probability that she selects zero evil players?

Input Specification

The first line contains an integer $G$, representing the number of distinct groups of players.

The next $G$ lines each contain two space separated integers $e_g$ and $p_g$, the number of evil players in the group, and the total players in the group respectively.

Constraints

$1\le G\le 1000$

$0\le e_g\le p_g$

$1\le p_g\le {10}^9$

Output Specification

Print the probability that she chooses zero evil players. Your answer will be considered correct if it is within ${10}^{-6}$ of the judge's answer.

Sample Input 1

2
2 4
1 2

Sample Output 1

0.25

Sample Input 2

2
0 10
10 10

Sample Output 2

0