Rectangle A B C D has sides \overline{A B} of length 4 and \overline{C B} of length 3. Divide \overline{A B} into 168 congruent segments with points A=P_{0}, P_{1}, \ldots, P_{168}=B, and divide \overline{C B} into 168 congruent segments with points C=Q_{0}, Q_{1}, \ldots, Q_{168}=B. For 1 \leq k \leq 167, draw the segments \overline{P_{k} Q_{k}}. Repeat this construction on the sides \overline{A D} and \overline{C D}, and then draw the diagonal \overline{A C}. Find the sum of the lengths of the 335 parallel segments drawn.