Let $i_1$, $i_2$, ..., $i_k$ be different elements of the set $\{1, 2, ..., n\}$. Permutation $a$ such that $a(i_j)=i_{j+1}$, $a(i_k)=i_1$ for any $j\in \{1, 2, ..., k - 1\}$, and $a(s)=s$ for any $s\notin \{i_1, i_2, ..., i_k\}$, is called a cycle of length $k$. Notation: $(i_1, i_2, ..., i_k)$. The set $\{i_1, ..., i_k\}$ is called the carrier of the cycle, and $k$ is called the length of the cycle.