Let a, b, and c be digits with a \neq 0. The three-digit integer a b c lies one third of the way from the square of a positive integer to the square of the next larger integer. The integer a c b lies two thirds of the way between the same two squares. What is a+b+c ?
Answer Choices
A. 10
B. 13
C. 16
D. 18
E. 21