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