Searching the Photo Library

A shop wants a "find similar products" search over its library of $N$ product photos. Each photo is $32 \times 32$ pixels in colour (3 channels), so it is $3072$ numbers.

Raw search. Each query photo is compared directly with every library photo, using one subtract-and-square per number.

Code search. An autoencoder has been trained. Its encoder squeezes a photo to a code of $32$ numbers through two fully connected layers, $3072 \to 256 \to 32$. The whole library was encoded once, overnight, and that cost is not counted here. At search time the query photo is run through the encoder, and its code is compared with every library code, using one subtract-and-square per number.

Count cost in operations. A fully connected layer from $n$ inputs to $m$ outputs costs $n \times m$ operations (ignore biases and activations), and one subtract-and-square costs one operation.

The speedup is the raw search's cost per query divided by the code search's cost per query.

What is the smallest library size $N$ for which the speedup is at least $80$?

Give the exact whole number.