D. The Child and Zootime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputOf course our child likes walking in a zoo. The zoo has n areas, that are numbered from 1 to n. The i-th area contains ai animals in it. Also there are m roads in the zoo, and each road connects two distinct areas. Naturally the zoo is connected, so you can reach any area of the zoo from any other area using the roads.Our child is very smart. Imagine the child want to go from area p to area q. Firstly he considers all the simple routes from p to q. For each route the child writes down the number, that is equal to the minimum number of animals among the route areas. Let's denote the largest of the written numbers as f(p, q). Finally, the child chooses one of the routes for which he writes down the value f(p, q).After the child has visited the zoo, he thinks about the question: what is the average value of f(p, q) for all pairs p, q (p ≠ q)? Can you answer his question?InputThe first line contains two integers n and m (2 ≤ n ≤ 105; 0 ≤ m ≤ 105). The second line contains n integers: a1, a2, ..., an (0 ≤ ai ≤ 105). Then follow m lines, each line contains two integers xi and yi (1 ≤ xi, yi ≤ n; xi ≠ yi), denoting the road between areas xi and yi.All roads are bidirectional, each pair of areas is connected by at most one road.OutputOutput a real number — the value of .The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.ExamplesInput4 310 20 30 401 32 34 3Output16.666667Input3 310 20 301 22 33 1Output13.333333Input7 840 20 10 30 20 50 401 22 33 44 55 66 71 45 7Output18.571429NoteConsider the first sample. There are 12 possible situations:  p = 1, q = 3, f(p, q) = 10.  p = 2, q = 3, f(p, q) = 20.  p = 4, q = 3, f(p, q) = 30.  p = 1, q = 2, f(p, q) = 10.  p = 2, q = 4, f(p, q) = 20.  p = 4, q = 1, f(p, q) = 10. Another 6 cases are symmetrical to the above. The average is .Consider the second sample. There are 6 possible situations:  p = 1, q = 2, f(p, q) = 10.  p = 2, q = 3, f(p, q) = 20.  p = 1, q = 3, f(p, q) = 10. Another 3 cases are symmetrical to the above. The average is .
Input4 310 20 30 401 32 34 3
Output16.666667
['dsu', 'sortings', '*1900']