RU-SPB 2020 Problem 97

Let $G$ be a graph with $400$ vertices. For any edge $AB$ we call a cuttlefish the set of all edges from $A$ and $B$ (including $AB$ ). Each edge of the graph is assigned a value of $1$ or $-1$ . It is known that the sum of edges at any cuttlefish is greater than or equal to $1$ . Prove that the sum of the numbers at all edges is at least $-10^4$ .