$N$ trolls are in a hole that is $D_N$ cm deep. The $n$-th troll is characterized by:

• the distance from his feet to his shoulders in cm, $h_n$
• the length of his arms in cm, $l_n$
• his IQ (Irascibility Quotient), $q_n$.

Trolls can pile up on top of each other, with each troll standing on the shoulders of the one below him. A troll can climb out of the hole and escape if his hands can reach to the surface. Once a troll escapes he cannot participate any further in the escaping effort.

The trolls execute an optimal strategy for maximizing the total IQ of the escaping trolls, defined as $Q(N)$.

Let
$r_n=[(5^{n}mod({10}^9+7))mod101]+50$
$h_n=r_{3n}$
$l_n=r_{3n+1}$
$q_n=r_{3n+2}$
$D_N=\frac{1}{\sqrt{2}}\sum _{n=0}^{N-1}{h}_n$.

For example, the first troll ($n=0$) is 51cm tall to his shoulders, has 55cm long arms, and has an IQ of 75.

You are given that $Q(5)=401$ and $Q(15)=941$.

Find $Q(1000)$.