Question 63
On a plane, $10^6$ points are marked no three of which are collinear; and all segments between these points are drawn. On each drawn segment Grisha placed a real number whose absolute value does not exceed $1$. Then for each six marked points, he calculated the sum of the numbers on all $15$ segments connecting these points. It turned out that the absolute value of each such sum is not less than $C$, and among such sums there exist both positive and negative sums. Find the greatest possible $C$.
(G. R. Chelnokov)
(G. R. Chelnokov)