Can you solve this chess problem of a lone knight against numerous opposing pieces? [FEN &quot;8/1nq5/bppp4/1p1k1K1N/1rrp3b/2pp2p1/8/n7 w - - 0 1&quot;]

I found this interesting and unique chess problem online.
Disclaimer: This is not necessarily a position from a game. It's just a beautiful composition wherein your objective as White is to checkmate the black king. White is moving from bottom to top and Black is moving from top to bottom.
This problem was composed by Hungarian Engineer Ottó Bláthy.
It's white turn and it's mate in 12 moves. Can you find the winning move continuation for white?
OK

The check must come from the knight (D'uh!)
The black king must be on c5 for the mate
The white king must be used to cover any empty squares to the right of the black king - thus the white king must move, thus there must be at least one non-checking move
On a non-checking move Black can try to release the prison by Ra4
The only way white can cover this is for the winning check to come from d3, as this covers b4 and the knight can not be captured there (unlike a6 after the rook moves)
When white makes the non-checking move he must be in a position to deal with threats from black, in particular the black queen, and checks from the black knight on c7 and the black bishop on h4
If on the non-checking move white plays Ke6 directly the knight check from d8 will break the prison
Thus the king must go to e4, attracting the black pawn to d5 with check, after which, if the black queen has been eliminated, the white king can go Ke6 Nd8+ Kd7 and it can't at that point be driven away

Putting this all together leads us to
[Event &quot;&quot;]
[Site &quot;&quot;]
[Date &quot;????.??.??&quot;]
[Round &quot;&quot;]
[White &quot;&quot;]
[Black &quot;&quot;]
[Result &quot;1-0&quot;]
[FEN &quot;8/1nq5/bppp4/1p1k1K1N/1rrp3b/2pp2p1/8/n7 w - - 0 1&quot;]

1.Nf4+ Kc5 2.Ne6+ Kd5 3.Nxc7+ Kc5 4.Nxa6+ Kd5 5.Nc7+ Kc5 6.Ne6+ Kd5 7.Nf4+
Kc5 8.Ke4 d5+ 9.Ke5 Bf6+ 10.Ke6 Nd8+ 11.Kd7 Ra4 12.Nxd3# 1-0

I think that's it, though I can't see at the moment what the Black Knight on a1 is doing