One particular permutation $\sigma $ of $5$ elements such that $\sigma ^{-1} (j) \le \sigma (j)$
Let $\sigma :\{1,2,3,4,5\} \rightarrow \{1,2,3,4,5\}$ be permutations such that $ \sigma^{-1}(j) \leq \sigma(j)~\forall j, 1 \leq j \leq 5$.