Promoting without tempo in this position leads to draw..But if White makes a mistake?

1.g4
[1.Kg2 a5 2.g4 a4 3.g5 a3 4.g6 a2 5.g7 a1Q 6.g8Q Draw as well; But, if 1.Kh3 Black will win 1...a5 2.g4 a4 3.g5 a3 4.g6 a2 5.g7 a1Q 6.g8Q Qh1+ 7.Kg4 Qg2+ X-ray attack 8.Kf4 Qxg8 Black will checkmate in a maximum of nine moves from here against any defense.]

1...a5 2.g5 a4 3.g6 a3 4.g7 a2 5.g8Q a1Q 6.Qf7+ Kb6 7.Qb3+ Kc5 8.Qc2+ Kb4 9.Qe4+ Ka3 10.Qa8+ Kb2
supporting the Queen..

11.Qb7+ Ka2 12.Qa6+ Kb2 13.Qxa1+ Kxa1
Draw due to insufficient material. 1/2-1/2

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