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Crazy position from a puzzle. Big material advantage, but hard to win against SF8.

What's the easiest way to convert the advantage in this position as white? It's from a puzzle I found quite hard. But the toughest part was playing the endgame against the computer at level 8. I tried several times and failed. After many tries, I had to play a super complicated endgame and sacrifice the queen to finally win. Can anyone do better? I think my endgame technique is better than my mid-game. That's probably why I struggled so much and only won when I got a clear position, but with less advantage than when I had the queen. If you find the first moves hard to find, it's because the position is a hard puzzle. You can use an engine to solve the puzzle and then you can play the resulting position, in which white has a Q and a B against R and N.

5rk1/4bppp/5n2/2pp4/4qP2/1Q3N2/1PP3PP/2B2RK1 w - - 0 19

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