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AMC 10B 2025 (Problem 9)

How many ordered triples of integers (x,y,z)(x,y,z) satisfy the following system of inequalities?
−x−y−z≤−2−x+y+z≤2x−y+z≤2x+y−z≤2\begin{aligned}-x-y-z&\le-2\\ -x+y+z&\le2\\ x-y+z&\le2\\ x+y-z&\le2\end{aligned}
(A)  4\text{(A)}\;4(B)  8\text{(B)}\;8(C)  11\text{(C)}\;11(D)  15\text{(D)}\;15(E)  17\text{(E)}\;17