Find the decisive blow (difficulty 1005)

12345678 hgfedcba

Black to move

Show solution
12345678 hgfedcba
  1. g2–h2 key move
  2. h1–h2
  3. c6–h1

What makes it

The win is mate in two, paid for with a 5-point investment. A fork: two or three pieces fall under attack together. Difficulty 1005: no gift.