Can you solve this chess problem of king and pawn against all opposing pieces? [FEN &quot;8/8/8/2p5/1pp5/brpp4/qpprpK1P/1nkbn3 w - - 0 1&quot;]

I found this interesting and unique chess problem online.
Disclaimer: This is not a plausible position from a game, however it is legal. 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 the Hungarian Engineer, Ottó Bláthy.
It's white's turn. Can you find the winning move continuation for white?
First,

 White takes the single mobile Black piece: 1. Kxe1

Then

 Black can only move their queen back and forth between a1 and a2.

Meanwhile

 the white pawn promotes to a knight, captures the c-pawns and then the b3 rook.

[FEN &quot;8/8/8/2p5/1pp5/brpp4/qpprpK1P/1nkbn3 w - - 0 1&quot;]

1. Kxe1 Qa1 2. h4 Qa2 3. h5 Qa1 4. h6 Qa2 5. h7 Qa1 6. h8=N Qa2 7. Ng6 Qa1 8. Ne5 Qa2 9. Nxc4 Qa1 10. Na5 c4 11. Nxc4 Qa2 12. Na5 Qa1 13. Nxb3#

However,

 Black can also play 10... Qa2 and the knight is unable to lose a tempo. The king is unable as well (because he needs to keep the e2 pawn under control); white's only piece capable of losing a tempo is the ... pawn, by not doing a double step on move 2!

So let's try
[FEN &quot;8/8/8/2p5/1pp5/brpp4/qpprpK1P/1nkbn3 w - - 0 1&quot;]

1. Kxe1 Qa1 2. h3 Qa2 3. h4 Qa1 4. h5 Qa2 5. h6 Qa1 6. h7 Qa2 7. h8=N Qa1 8. Ng6 Qa2 9. Ne5 Qa1 10. Nd7 Qa2 11. Nxc5 Qa1 12. Na4 Qa2 13. Nb6 Qa1 14. Nxc4 Qa2 15. Na5 Qa1 16. Nxb3#