Consider a random permutation of the set $\{1, 2, . . . , 2015\}$. In other words, for each $1 \le i \le 2015$, $i$ is sent to the element $a_i$ where $a_i \in \{1, 2, . . . , 2015\}$ and if $i \neq j$, then $a_i \neq a_j$. What is the expected number of ordered pairs $(a_i, a_j )$ with $i - j > 155$ and $a_i - a_j > 266$?


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