Sorting Vases

Chef has $N$ vases in a row (numbered $1$ through $N$, initially from left to right). He wants to sort them in a particular order which he finds the most beautiful. You are given a permutation $p_1, p_2, \ldots, p_N$ of the integers $1$ through $N$; for each valid $i$, Chef wants the $i$-th vase to end up as the $p_i$-th vase from the left. In order to achieve this, Chef can swap vases. Any two