Can you solve this unique chess problem of white's two queens vs black's six rooks? [FEN &quot;3Q4/7Q/3rp3/2rkr3/2rrr3/7K/8/8 w - - 0 1&quot;]

I found this interesting and unique chess problem online, 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 made by Filip Bondarenko and published in Feenschach in 1960, although this version is cut one move short.
White to move. Can anyone solve this?
It's checkmate in 20 moves. White's queens circle around the board giving checks, and Black interposes horizontally/vertically moving pieces. Black only has one choice because the other piece is pinned from the previous check. That goes well, until the pawn needs to move sideways:
[FEN &quot;3Q4/7Q/3rp3/2rkr3/2rrr3/7K/8/8 w - - 0 1&quot;]

1. Qb7+ Rc6 2. Qa5+ Rc5 3. Qb3+ Rc4 4. Qd2+ Rd4 5. Qf3+ Re4 6. Qg5+ e5 7. Qf7+ Re6 8. Qd8+ Rd6
9. Qb7+ Rc6 10. Qa5+ Rc5 11. Qb3+ Rc4 12. Qd2+ Rd4 13. Qf3+ e4 14. Qg5+ Re5 15. Qf7+ Re6 16. Qd8+ Rd6
17. Qb7+ Rc6 18. Qa5+ Rc5 19. Qb3+ Rc4 20. Qd2# 1-0