Let $a_1, a_2, \ldots, a_{100}$ be positive integers, satisfying $$\frac{a_1^2+a_2^2+\ldots+a_{100}^2} {a_1+a_2+\ldots+a_{100}}=100.$$ What is the maximal value of $a_1$? 

Let's think step by step and output the final answer within \boxed{}.
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