There Are 71 Perfect Squares Less Than 5050

Let \(a_1, a_2, \ldots, a_{100}\) be a permutation of the numbers \(1,2,3, \ldots ,100\).

Let \(S_i=a_1+a_2+\cdots +a_i\).

What is the maximum number of perfect squares among the numbers \(S_1,S_2, \ldots ,S_{100}\)?

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