We show by a dynamical argument that there is a positive integer valued function $q$ defined on positive integer set $mathbb N$ such that $q([log n]+1)$ is a super-polynomial with respect to positive $n$ and [liminf_{nrightarrowinfty} rleft((2n+1)^2, q(n)right)<infty,] where $r( , )$ is the opposite-Ramsey number function.
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