# 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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