TUYMAADA 2020 Problem 3

Each edge of a complete graph with $101$ vertices is marked with $1$ or $-1$ . It is known that absolute value of the sum of numbers on all the edges is less than $150$ . Prove that the graph contains a path visiting each vertex exactly once such that the sum of numbers on all edges of this path is zero.

(Y. Caro, A. Hansberg, J. Lauri, C. Zarb)