CMO 1992 Problem 2

Given nonnegative real numbers $x_1,x_2,\dots ,x_n$ , let $a=min\{x_1, x_2,\dots ,x_n\}$ . Prove that the following inequality holds: $$\sum^{n}_{i=1}\dfrac{1+x_i}{1+x_{i+1}}\le n+\dfrac{1}{(1+a)^2}\sum^{n}_{i=1}(x_i-a)^2 (x_{n+1}=x_1),$$ and equality occurs if and only if $x_1=x_2=\dots =x_n$ .