A discrete mathematics problem by soumyaranjan ram

On a large \( 999 \times 999 \) board, each cell is colored either white or black.

Define a coordinated triple of cells \( (C_1, C_2, C_3 ) \) as the formation such that

  • \(C_1\) and \(C_2\) are in the same row;
  • \(C_2 \) and \(C_3\) are in the same column;
  • \(C_1\) and \(C_3\) are white;
  • \( C_2 \) is black.

What is the maximum number of coordinated triples? Enter your answer as the last three digits of that maximum.

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