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 \( S_1,S_2, \cdots , S_n \).

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