Rectangle \(ABCD_{}^{}\) has sides \(\overline {AB}\) of length 4 and \(\overline {CB}\) of length 3. Divide \(\overline {AB}\) into 168 congruent segments with points \(A_{}^{}=P_0, P_1, \ldots, P_{168}=B\), and divide \(\overline {CB}\) into 168 congruent segments with points \(C_{}^{}=Q_0, Q_1, \ldots, Q_{168}=B\). For \(1_{}^{} \le k \le 167\), draw the segments \(\overline {P_kQ_k}\). Repeat this construction on the sides \(\overline {AD}\) and \(\overline {CD}\), and then draw the diagonal \(\overline {AC}\). Find the sum of the lengths of the 335 parallel segments drawn.

(第九届AIME1991 第2题)