Let $ n>1$ be an odd integer and define: \[ N=\{-n,-(n-1),\dots,-1,0,1,\dots,(n-1),n\}.\] A subset $ P$ of $ N$ is called basis if we can express every element of $ N$ as the sum of $ n$ different elements of $ P$. Find the smallest positive integer $ k$ such that every $ k-$elements subset of $ N$ is basis.