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Let n be a positive integer. How many integer solutions (i, j, k, l) , \ 1 \leq i, j, k, l \leq n, does the following system of inequalities have:

1 \leq  -j + k + l  \leq  n 1  \leq  i - k + l  \leq  n 1  \leq  i - j + l  \leq  n 1  \leq  i + j - k  \leq  n \ ?

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