The coefficients of the polynomial 
\[P(x) = b_{10} x^{10} + b_9 x^9 + b_8 x^8 + \dots + b_2 x^2 + b_1 x + b_0 = 0\] 
are all integers, and its roots \(s_1, s_2, \dots, s_{10}\) are all integers. Furthermore, the roots of the polynomial 
\[Q(x) = b_0 x^{10} + b_1 x^9 + b_2 x^8 + \dots + b_8 x^2 + b_9 x + b_{10} = 0\] 
are also \(s_1, s_2, \dots, s_{10}\). Find the number of possible multisets \(T = \{s_1, s_2, \dots, s_{10}\}\). 
(A multiset, unlike a set, can contain multiple elements. For example, \(\{-3, -3, 6, 6, 6\}\) and \(\{6, -3, 6, 6, -3\}\) are the same multiset, but both are different from \(\{-3, 6, 6, 6\}\). And as usual, \(b_{10} \neq 0\) and \(b_0 \neq 0\).) Let's think step by step and output the final answer within \boxed{}.
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