IMO LL Inequality problem

[sirio11]

This was proposed by USA for IMO 1979, it did not make the short list (LL stands for long list), but I think it's a good inequalities problem.

If a_1,a_2,...,a_n denote the length of the sides of an arbitrary n-gon, prove that:

[n/(n-1)] <= [a_1/(S - a_1)] + [a_2/(S - a_2)] +..... + [a_n/(S - a_n)] <= 2


where S = a_1 + a_2 +......+ a_n