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Can You Find The Shortest Mate

How quickly can you find the shortest mate from the position above? It took me almost half an hour.

8/7p/7R/1p2kp2/1R6/3K4/8/8 w - - 0 1

It took me 13 minutes.

1.Rbh4 Kd5
2.Rd4+ Kc5
3.Rf4 b4

Alena, I left you an important message in one of the Zinar puzzles.

R a6 ?