Why is the Rabin mapping not a permutation over $\mathbb{Z}_N^*$

Why is the Rabin mapping: $$f_i(x_i)=x_i^2 \bmod N_i$$ not a Permutation over $$\mathbb{Z}_N^*$$?

Why is the Rabin mapping: $$f_i(x_i)=x_i^2 \bmod N_i$$ not a Permutation over $$\mathbb{Z}_N^*$$?
For example, $$f_i(1) = f_i(N_i - 1)$$, with both being 1
• or, general case: $f_i(j) = f_i(N-j)$ – kelalaka Dec 10 '18 at 8:31