CWMO 2002 Problem 6

Given a positive integer $n$ , find all integers $(a_{1},a_{2},\cdots,a_{n})$ satisfying the following conditions: $(1): a_{1}+a_{2}+\cdots+a_{n}\ge n^2;$ $(2): a_{1}^2+a_{2}^2+\cdots+a_{n}^2\le n^3+1.$