Let the roots of \(x^{2022} - 7x^{2021} + 8x^2 + 4x + 2\) be \(r_1, r_2, \ldots, r_{2022}\), the roots of \(x^{2022} - 8x^{2021} + 27x^2 + 9x + 3\) be \(s_1, s_2, \ldots, s_{2022}\), and the roots of \(x^{2022} - 9x^{2021} + 64x^2 + 16x + 4\) be \(t_1, t_2, \ldots, t_{2022}\). Compute the value of:
\[
\sum_{1 \le i,j \le 2022} r_i s_j + \sum_{1 \le i,j \le 2022} s_i t_j + \sum_{1 \le i,j \le 2022} t_i r_j.
\]

Let's think step by step and output the final answer within \boxed{}.
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