A single snowflake rests at the origin, \((0, 0)\), on an infinite cartesian plane. At time \(t = 0\), it divides and replicates itself, moving exactly \(1\) unit in each of the \(8\) major compass directions (N, NE, E, SE, S, SW, W, and NW), leaving \((0, 0)\) vacant.

###### Image Credit: http://www.featurepics.com/online/White-Snowflakes-Blue-1406139.aspx

At \(t = 1\), all snowflakes which occupy the *exact* same points are merged into one, and then the process repeats for every snowflake, resulting in the following pattern:

So, to iterate the first few steps:

- There is \(1\) snowflake at time \(t = 0\)
- At time \(t = 1\), there are \(8\) snowflakes pre-merge.
- No snowflakes coincide, so there are \(8\) snowflakes post-merge as well.
- At time \(t = 2\), there are \(64\) snowflakes pre-merge.
- Post-merge, only \(33\) snowflakes remain.

How many snowflakes are there at time \(t = 1000\), post-merge?

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