An m \times n \times p rectangular box has half the volume of an (m+2) \times(n+2) \times(p+2) rectangular box, where m, n, and p are integers, and m \leq n \leq p. What is the largest possible value of p ?
An m \times n \times p rectangular box has half the volume of an (m+2) \times(n+2) \times(p+2) rectangular box, where m, n, and p are integers, and m \leq n \leq p. What is the largest possible value of p ?