Let $a _ { 0 } , a _ { 1 } , \ldots , a _ { 23 }$ be real numbers such that
$$\left( 1 + \frac { 2 } { 5 } x \right) ^ { 23 } = \sum _ { i = 0 } ^ { 23 } a _ { i } x ^ { i }$$
for every real number $x$. Let $a _ { r }$ be the largest among the numbers $a _ { j }$ for $0 \leq j \leq 23$.\\
Then the value of $r$ is $\_\_\_\_$.