Lexicographically smallest cyclic shift

A permutation of length $n$ is a sequence of pairwise distinct positive integers p_1, p_2, \ldots, p_n, where 1 \le p_i \le n for each $i$. We say that the permutation q_1, q_2, \ldots, q_n is lexicographically less than the permutation p_1, p_2, \ldots, p_n if there exists $i$ such that q_i < p_i and for all j < i we have p_j = q_j.

A cyclic shift by $k$ of the permutation p_1, p_2, \ldots, p_n is the sequence p_{k+1}, p_{k+2}, \ldots, p_n, p_1, \ldots, p_k. Note that any cyclic shift of a permutation is also a permutation.

Find the lexicographically smallest cyclic shift of the given permutation.