The sum of the following seven numbers is exactly 19 :
\begin{gathered}
a_{1}=2.56, \quad a_{2}=2.61, \quad a_{3}=2.65, \quad a_{4}=2.71, \\
a_{5}=2.79, \quad a_{6}=2.82, \quad a_{7}=2.86 .
\end{gathered}
It is desired to replace each a_{i} by an integer approximation A_{i}, \quad 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” \left|A_{i}-\mathrm{a}_{i}\right|, is as small as possible. For this minimum M, what is 100 M ?