Can you solve this queen + 3 pawns vs bishop + 3 pawns chess problem? [FEN &quot;7k/8/8/8/6p1/4QpPb/5PpP/6K1 w - - 0 1&quot;]

I found this interesting and unique chess problem online while surfing on the internet.
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 the Hungarian Engineer, Ottó Bláthy.
It's White's turn. Can you find the winning move continuation for White?
If White can get the Black king to the first rank, then it will not be fast enough to catch the g-pawn from promoting.  White starts by playing 1. Qg5, and after 1...Kh7 2. Qf6 Kg8 3. Qh6, the White queen can simply imitate the Black king's movements until she can start forcing the king down towards the first rank.
[FEN &quot;7k/8/8/8/6p1/4QpPb/5PpP/6K1 w - - 0 1&quot;]


 1. Qg5 Kh7 2. Qf6 Kg8 3. Qh6 Kf7 4. Qg5 Kf8 5. Qg6 Ke7 6. Qf5 Ke8 7. Qf6 Kd7 8. Qe5 Kd8 9. Qe6 Kc7 10. Qd5 Kc8 11. Qd6 Kb7 12. Qc5 Kb8 13. Qc6 Ka7 14. Qc8 Kb6 15. Qd7 Ka6 16. Qc7 Kb5 17. Qd6 Ka5 18. Qc6 Kb4 19. Qd5 Ka4 20. Qc5 Kb3 21. Qd4 Ka3 22. Qc4 Kb2 23. Qd3 Ka2 24. Qc3 Kb1 25. Qh8 Kc2 26. Qxh3

As to whether this is the fastest win, I'm not sure.