In geometry, a tesseract or 4-cuboid is a four-dimensional hypercuboid, analogous to a two-dimensional rectangle and a three-dimensional cuboid. We have a Tesseract with dimensions $a$, $b$, $c$, and $d$.

Bob and Alice are playing a game with the Tesseract. In one move, a player can perform the following action:

They choose one dimension $s$ out of the four of the Tesseract. They change the dimension to $i$ units. This move is only allowed if:

gcd($s$, $s - i$) = $s - i$ and $i < s$ and $i > 0$

For example, they can change the dimension of length $8$ to a dimension of length $7, 6$ or $4$.

Both players are smart, so it is assumed they play optimally. The player who cannot perform a move loses.

Let $F(n)$ indicate the number of sets of dimensions $(a, b, c, d)$ where $1 \leq a, b, c, d \leq n$ such that Alice wins if Bob starts the game. Two sets are considered different if any one of the dimensions is not the same in both sets. For example, $(1,2,1,1)$ and $(2,1,1,1)$ are different sets.

Find $F(324325346214122)\mod 987654321$.