# $HAM-NO-HAM$ problem: How do I show reduction from $HAMcircuit$ problem to the following problem?

consider the following language: $HAM-NO-HAM=\{(G_1,G_2)|G_1, G_2\}$ are undirected graphs, $G_1$ has a Hamilton and $G_2$ doesn't have one$\}$.

i need to decide wheter it's in $P, NP, CONP$ or none of the above.

If I'll show reductions from $HAMcircuit$ and from $NO-HAMcircuit$ I will get that $HAM-NO-HAM$ is both $NPC$ and $coNPC$.

What is the best way for showing a reduction from the $HAMcircuit$ to $HAM-NO-HAM$?

I want somehow to copy it and then I would get the graph which does or doesn't have a $HAMcircuit$ but I need to copy it again so it would fit the other other condition for the second graph.

Any suggestion?

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