On a $n \times n$ grid, each edge are written with $=$ or $\neq$. We need to filled every cells with color black or white. Find the largest constant $k$, such that for every $n>777771449$ and any layout of $=$ and $\neq$, we can always find a way to colored every cells, such that at least $k \cdot 2n(n-1)$ neighboring cells, there colors conform to the symbols on the edge. (Namely, two cells are filled with the same color if $=$ was written on their edge; two cells are filled with different colors if $\neq$ was written on their edge) Proposed by chengbilly & sn6dh