CWMO 2013 Problem 7

Label sides of a regular $n$ -gon in clockwise direction in order 1,2,..,n. Determine all integers n ( $n\geq 4$ ) satisfying the following conditions: (1) $n-3$ non-intersecting diagonals in the $n$ -gon are selected, which subdivide the $n$ -gon into $n-2$ non-overlapping triangles; (2) each of the chosen $n-3$ diagonals are labeled with an integer, such that the sum of labeled numbers on three sides of each triangles in (1) is equal to the others;