The sum of the following seven numbers is exactly 19:


It is desired to replace each \(a_{i}\) by an integer approximation \(A_{i},1\leq i\leq 7\), so that the sum of the \(A_{i}\)'s is also 19, and so that \(m\), the maximum of the errors \(\mid A_{i}-a_{i}\mid\), is as small as possible. For this minimum \(m\), What is \(100m\)?

(第三届AIME1985 第8题)