I was trying to solve the question http://mirror.codeforces.com/contest/117/problem/E I coded it but in one of the test cases my answer is differing from jury but i think that the jury's answer is not in accordance with the question ( I know that i am wrong because many people have got ac on that problem ) so i request the commumnity to solve my doubt.In the last case where the path from 5 to 6 is asked there are two paths 5 -> 6 5 -> 4 -> 3 -> 6 the smallest one is the first one while the lexicographically smallest one is the second one.The question asks to find the smallest path first so 5->6 shold be taken and the number of components is 5 which are {3},{4},{5,6},{1},{2} but the answer is 3 which is got when we take the second path ? Why . The first sample case is itself against this.

The test i am refering to is this. 6 4 6 3 4 3 1 5 1 2 5 4 5 6 1 1 3 3 5 2 5 6

PLEASE HELP!!