Permutation and perfect square

Let $a_1,a_2,\cdots , a_n$ be a permutation of the numbers $1,2, \cdots , n$ . Let $S_i= \sum_{j=1}^{i}a_j$ for $1 \le i \le n$ . Find the smallest positive integer $n$ such that there are at least $60$ perfect squares among the numbers $S_1,S_2, \cdots , S_n$ .