No coders from QuantumLand qualified to the semifinal but its not stopping them from creating problems!

There are cities in QuantumLand. Each of the cities may have a one-way road toward another city. QuantumLand is strange, and nothing is certain here; sometimes a road will exist, sometimes it won't!

Given the description of all the cities and roads in QuantumLand and the probability of each road's existence, can you determine the expected number of cycles formed in QuantumLand?

Note: A cycle of length m is is a sequence of nodes such that for every , there is an edge between and . The length of any cycle is at least 2.

Input Format

First line will have an integer . Each of the next lines will have two integers and . Each line denotes that there is a one-way road from city to city with probability.

Constraints




All the inputs are integer numbers.

Output Format

Print a single line, the number of expected cycles in QuantumLand. Print exactly two digits after the decimal point rounded to the nearest decimal place. For example, if the answer is "12.555", you should print "12.56".

Sample Input

3
3 80
1 90
2 100

Sample Output

0.72

Explanation

The graph in the sample input looks like this:

Line: 1 Col: 1
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