Question 7
In each cell of a $1 \times 2007$ board of consecutive cells one must write an integer from $1$ to $2007$, without repeating numbers. Then the following $2007$ numbers are considered: the number in the first cell from the left; the sum of the numbers in the first two cells (from the left); the sum of the numbers in the first three cells; ...; the sum of the numbers in the first $2006$ cells and the sum of the numbers in all the cells. For each of these $2007$ numbers that leaves remainder $5$ when divided by $6$, one earns $1$ peso. What is the maximum amount of money that can be earned?