CF690F2 Tree of Life (medium)

Heidi got tired of deciphering the prophecy hidden in the Tree of Life and decided to go back to her headquarters, rest a little and try there. Of course, she cannot uproot the Tree and take it with her, so she made a drawing of the Tree on a piece of paper. On second thought, she made more identical drawings so as to have $ n $ in total (where $ n $ is the number of vertices of the Tree of Life) – who knows what might happen? Indeed, on her way back Heidi was ambushed by a group of zombies. While she managed to fend them off, they have damaged her drawings in a peculiar way: from the $ i $ -th copy, the vertex numbered $ i $ was removed, along with all adjacent edges. In each picture, the zombies have also erased all the vertex numbers and relabeled the remaining $ n-1 $ vertices arbitrarily using numbers $ 1 $ to $ n $ (fortunately, each vertex still has a distinct number). What's more, the drawings have been arbitrarily shuffled/reordered. Now Heidi wants to recover the Tree of Life from her descriptions of all the drawings (as lists of edges).

The first line of the input contains $ Z

If Heidi's drawings cannot possibly come from a single tree, you should output the word NO. Otherwise, output one line containing the word YES and $ n-1 $ lines describing any tree that Heidi's drawings could have come from. For every edge you should output the numbers of the vertices that it connects, separated with a single space. If there are many solutions, print any of them.