Fill a 3 by 3 grid with the digits 1 to 9 using the following five rules:

1. The sum of the top row is twice the sum of the center row.

2. The sum of the left column is twice the sum of the center column.

3. The sum of the right column plus twice the sum of the bottom row is equal to the sum of the whole grid.

4. The sum of the bottom row plus twice the sum of the right column is not equal to the sum of the whole grid.

5. The top row is the only row with both odd and even numbers.

Show that there is only one solution.