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1 – Rxh7+ If 1 – Kxh7
Then 2 – Rh1+ If 2 – Kg8
Then 3 – Ng5+ – Kf8
4 – Rh8#
1 – Rxh7+ If 1 – Kxh7
Then 2 – Rh1+ If 2 – Kg6
Then 3 – Qh5#
1 – Rxh7+ If 1 – Kxh7
Then 2 – Rh1+ If 2 – Bh4
Then 3 – Rxh4+ If 3 – Kg8
Then 4 – Ng5+ – Kf8
Rh8#
1 – Rxh7+ If 1 – Kxh7
Then 2 – Rh1+ If 2 – Bh4
Then 3 – Rxh4+ If 3 – Kg6
Then 4 – Nxf4+ – Kg6
Bd4#
1. Rxh7+ Kxh7 ( 1. … Kg8 2. Ng5+ Kf8 3. Rh8# or Qf7#)
2. Rh1+ Bh4 ( 2. .. Kg6 3. Nxf4# or Qh5# )
3. Rxh4+ Kg8 ( 3. … Kg6 4. Nxf4+ Kf6 5. Bd4# )
4. Ng5+/Nd8+ Kf8 ( 4. Nc7/Nd4/Nf8 Kf8 5. Rh8# )
5. Qf7# or Rh8#
1. Rxh7+. Kxh7. (If Kg8. 2. Ng5/f8+. Kf8. 3. Rh8#)
2. Rh1+. Bh4. ( If Kg8. 3. Ng5/f8+. Kf8. 4. Rh8# or 2. Kg6. 3. Qh5#)
3. Rxh4+. Kg6. (If Kg8. 4. Ng5/f8+. Kf8. 5. Rh8#)
4. Qg5+. Kf7.
5. Qxg7+. Kxe6. (If Ke8. 6. Qe7#)
6. Rh6+. Kf5.
7. Qf6#
I would have looked at Rxh7 in any case, but the fact that it is the only check and the only defense to getting mated at a2 makes the first move easy to find.