CMO 1995 Problem 1

Let $a_1,a_2,\cdots ,a_n; b_1,b_2,\cdots ,b_n (n\ge 3)$ be real numbers satisfying the following conditions: (1) $a_1+a_2+\cdots +a_n= b_1+b_2+\cdots +b_n$ ; (2) $0<a_1=a_2, a_i+a_{i+1}=a_{i+2}$ ( $i=1,2,\cdots ,n-2$ ); (3) $0<b_1\le b_2, b_i+b_{i+1}\le b_{i+2}$ ( $i=1,2,\cdots ,n-2$ ). Prove that $a_{n-1}+a_n\le b_{n-1}+b_n$ .