7. The numbers $a, b$, and $c$ were written on the board. They were erased, and in their place, the numbers $a-2, b+2, c^{2}$ were written. It turned out that the numbers on the board were the same as those initially written (possibly in a different order). What values can the number $a$ take, given that the sum of the numbers $a, b$, and $c$ is 2006? If necessary, round the answer to the hundredths.
Answer: 1004 or 1003.5.