Educational Round 27 : G question , Need help.

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while learning from tutorial, I was able to understand first paragraph clearly. I can also see that we just need to find out elementary cycles in graph(which can be done with [**how to find primary cycles in undirected graph ?** ](https://www.quora.com/How-can-we-find-all-simple-cycles-in-an-undirected-graph-efficiently-How-do-I-find-the-points-that-are-forming-a-cycle-in-a-graph) , an answer written by **Aditya Prakash**) . ↵
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Now I am not able to grasp how does gaussian method works. I have also tried to look into some solutions like, [born2rule](http://codeforces.com/contest/845/submission/29683752) , [rajat1603](http://codeforces.com/contest/845/submission/29656636) , [shubhamgoyal__](http://codeforces.com/contest/845/submission/29654510) . all this solutions look very similar, which uses gaussian method. ↵
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so , can someone help me out with gaussian method ? what it actually does ? and when can we use it ?