CMO 2012 Problem 4

Let $f(x)=(x + a)(x + b)$ where $a,b>0$ . For any reals $x_1,x_2,\ldots ,x_n\geqslant 0$ satisfying $x_1+x_2+\ldots +x_n =1$ , find the maximum of $F=\sum\limits_{1 \leqslant i < j \leqslant n} {\min \left\{ {f({x_i}),f({x_j})} \right\}}$ .