The sum of the following seven numbers is exactly 19:

$$a_{1}=2.56,a_{2}=2.61,a_{3}=2.65,a_{4}=2.71,a_{5}=2.79,a_{6}=2.82,a_{7}=2.86$$

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)