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: $$\begin{array}{rl}{S}_0& =290797\\ S_t& =S_{t-1}^{2}mod50515093& t>0\end{array}$$ 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 $20\le y\le 47$, 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 $12\to 1\to 2\to \cdots$.

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 $C({10}^5)$.