Clock Grid (noch nicht ├╝bersetzt)

Problem 790

There is a grid of length and width 50515093 points. A clock is placed on each grid point. The clocks are all analogue showing a single hour hand initially pointing at 12.

A sequence $S_t$ is created where: $$ \begin{align} S_0 &= 290797\\ S_t &= S_{t-1}^2 \bmod 50515093 &t>0 \end{align} $$ The four numbers $N_t = (S_{4t-4}, S_{4t-3}, S_{4t-2}, S_{4t-1})$ represent a range within the grid, with the first pair of numbers representing the x-bounds and the second pair representing the y-bounds. For example, if $N_t = (3,9,47,20)$, the range would be $3\le x\le 9$ and $20\le y\le47$, and would include 196 clocks.

For each $t$ $(t>0)$, the clocks within the range represented by $N_t$ are moved to the next hour $12\rightarrow 1\rightarrow 2\rightarrow \cdots $.

We define $C(t)$ to be the sum of the hours that the clock hands are pointing to after timestep $t$.
You are given $C(0) = 30621295449583788$, $C(1) = 30613048345941659$, $C(10) = 21808930308198471$ and $C(100) = 16190667393984172$.

Find $C(10^5)$.