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