2002 AMC 12P Problem 13

What is the maximum value of n for which there is a set of distinct positive integers k_1, k_2, ... k_n for which

k^2_1 + k^2_2 + ... + k^2_n = 2002?

\text{(A) }14 \qquad \text{(B) }15 \qquad \text{(C) }16 \qquad \text{(D) }17 \qquad \text{(E) }18

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.