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 $S_1,S_2, \ldots ,S_{100}$ ?