69th Belarusian Mathematical Olympiad

The medians $A{A}_1$ and $B{B}_1$ of the triangle $ABC$ intersect at the point $G$. Let $M$ and $N$ be the midpoints of the segments $GA$ and $GB$, and let $K$ and $L$ be the midpoints of the segments $C{B}_1$ and $C{A}_1$, respectively. The segments $KN$ and $LM$ intersect at the point $S$. Find the ratio $CS:SG$.