Does a defendant have a right to challenge his conviction for depraved indifference murder by requesting that the jury be charged with manslaughter in the second degree?

We reject the contention that defendant forfeited his right to challenge the sufficiency of his conviction for depraved indifference murder by requesting that the jury be charged on the lesser-included offense of manslaughter in the second degree, which requires a finding of recklessness. "Depraved indifference" is an additional core statutory requirement of depraved indifference murder, beyond mere recklessness and risk (see People v. Suarez, 6 N.Y.3d 202, 214-215, 811 N.Y.S.2d 267, 844 N.E.2d 721 [2005]).