Problem:
Network Reliability

An undirected graph is given.
Each edge of the graph disappears with a constant probability.
Calculate the probability with which the remained graph is connected.

Input

The first line contains three integers N (1 \leq N \leq 14), M (0 \leq M \leq 100) and P (0 \leq P \leq 100), separated by a single space.
N is the number of the vertices and M is the number of the edges. P is the probability represented by a percentage.

The following M lines describe the edges.
Each line contains two integers v_i and u_i (1 \leq u_i, v_i \leq N).
(u_i, v_i) indicates the edge that connects the two vertices u_i and v_i.

Output

Output a line containing the probability with which the remained graph is connected.
Your program may output an arbitrary number of digits after the decimal point. However, the absolute error should be 10^{-9} or less.

Sample Input 1

3 3 50
1 2
2 3
3 1

Output for the Sample Input 1

0.500000000000

Sample Input 2

3 3 10
1 2
2 3
3 1

Output for the Sample Input 2

0.972000000000

Sample Input 3

4 5 50
1 2
2 3
3 4
4 1
1 3

Output for the Sample Input 3

0.437500000000

Solution in Ruby (judge verdict: Time Limit Exceeded)

require 'set'

n, m, P = gets.split.map(&:to_i)

edges = Hash.new(1)
m.times do
    u, v = gets.split.map(&:to_i)
    key = Set[u, v]
    edges[key] *= P / 100.0
end


def f(edges, n)
    return 1.0 if n == 1
    return 0.0 if ! connected(edges, n)
    e = edges.keys[0]
    u0, v0 = e.to_a
    q = edges[e]

    deleted = edges.dup
    deleted.delete(e)

    contracted = Hash.new(1)
    edges.each do |f, prob|
        next if f == e
        u, v = f.to_a
        u = u0 if u == v0
        v = u0 if v == v0
        key = Set[u, v]
        contracted[key] *= prob
    end

    return q * f(deleted, n) + (1-q) * f(contracted, n-1)
end


def connected(edges, n)
    return true if n == 1
    return false if edges.size < n - 1
    components = []
    edges.each_key do |key|
        u, v = key.to_a
        cc1 = components.find {|cc| cc.include?(u)}
        cc2 = components.find {|cc| cc.include?(v)}
        if !cc1 && !cc2
            components << Set[u, v]
        elsif cc1 && cc2
            if cc1 != cc2
                cc2.each {|w| cc1 << w}
                components.delete(cc2)
            end
        elsif cc1
            cc1 << v
        else
            cc2 << u
        end
    end
    !components.empty? && components[0].size == n
end

printf("%.10f\n", f(edges, n).to_f)