Problem of the Week 984

A Black and White Issue

In a 984 x 984 square grid, each square is colored either white or black. Each black square not on the border has exactly five white squares among its eight neighbors. Each white square not on the border has exactly four black squares among its eight neighbors. How many black squares are there?

Source: an old Estonian Mathematical Olympiad (Crux Mathematicorum, Feb. 2003)