Consider we have three processes, P1, P2, P3, executed during last 5 minutes.

The execution of P1 consists of the alternation of 3 CPU bursts, c11, c12, c13, and 3 I/O bursts, d11, d12, d13. For each CPU burst c1i and I/O burst d1j, there exists a waiting time wc1ij. Likewise, for each I/O burst d1i and CPU burst c1j, there exists a waiting time wd1ij.

The execution of P2 consists of the alternation of 4 CPU bursts, c21, c22, c23, c24, and 2 I/O bursts, d21, d22. For each CPU burst c2i and I/O burst d2j, there exists a waiting time wc2ij. Likewise, for each I/O burst d2i and CPU burst c2j, there exists a waiting time wd2ij.

The execution of P3 consists of the alternation of 2 CPU bursts, c31, c32, and 4 I/O bursts, d31, d32, d33, d34. For each CPU burst c3i and I/O burst d3j, there exists a waiting time wc3ij. Likewise, for each I/O burst d3i and CPU burst c3j, there exists a waiting time wd3ij. For example, the total time P1 spent in the system consists of c11, wc111, d11, wd112, c12, wc122, d12, wd123, c13, wc133, d13.

Write an expression that represents the total execution period of all processes in the system during last 5 minutes.