With My Range Am I a Baritone or Tenor?

My exact range is from a C2 to a E4 without going into falsetto(since falsetto doesn't count for male singers right?). To break it down I sing from C2 toC3 in full chest voice. I sing from D3 to B4 in my middle or mixed voice. I sing from c4 to E4 in my head voice. I sing from Ef4 to A5 in falsetto