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Find The Shortest Mate

How quickly can you find the shortest mate in this position? I found the first move eay, but it was harder after that.

Q7/1K6/R7/8/4P3/8/6pp/7k w - - 0 1

V-1
1.e5 Kg1
2.Qa7+ Kf1
3.Ra2 g1=Q
4.Qa6+ Ke1
5.Qe2#

V-2
1.e5 Kg1
2.Qa7+ Kh1
3.Qe3 g1=Q
4.Qf3+ Qg2
5.Ra1#

V-3
1.e5 g1=Q
2.Kc7+ Qg2
3.Ra1#

V-4
1.e5 Kg1
2.Qa7+ Kh1
3.Qe3 g1=N
4.Rg6 any move
5.Qf3#

I think it isn't the shortest mate. I will think further.

At last I guessed how to mate in 3.

V-1
1.Qf8 g1=Q
2.Qf3+ Qg2
3.Ra1#

V-2
1.Qf8 g1=N
2.Rg6! Ne2
3.Qf3#

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