Chessboard Colouring

How many different colorings of a \(10 \times 10\) square grid are there such that the following 2 conditions are met?

  1. Each square must be either black or white.
  2. Each \(2 \times 2\) square in the grid must contain an odd number of \(1 \times 1\) black squares.

An example of how the grid can be colored

An example of how the grid can be colored

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