Let $M_1$ and $M_2$ be two matrices. What is the relationship between $tr(M_1M_2M_1M_2)$ and $tr(M_1^2 M_2^2 )$?

P.S. I tried a few examples and found $$ tr(M_1M_2M_1M_2) \le tr(M_1^2 M_2^2 ) $$ seems always true. Is there a theorem?