QuantumLand
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:
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with Ada.Text_IO, Ada.Integer_Text_IO;
use Ada;
procedure Solution is
-- Enter your code here. Read input from STDIN. Print output to STDOUT
end Solution