From 1999 IMO. Let \(n\geq 2\) be an integer. Determine the least possible constant \(C\) such that the inequality: \[\sum_{1\leq i<j\leq n} x_ix_j(x_i^2 + x_j^2) \leq C(\sum_{1\leq i\leq n}x_i)^4\] holds for all non-negative real numbers \(x_i\). For this constant \(C\) find out when the equality holds.