Permutation and perfect square

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


The answer is 100.

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