IMO 1966 LL USS51

In a school, n children numbered 1 to n are initially arranged in

IMO 1966 LL USS51

Origin: USS

Problem

In a school, n children numbered 1 to n are initially arranged in the order 1, 2, . . . , n. At a command, every child can either exchange its position with any other child or not move. Can they rearrange into the order n, 1, 2, . . . , n −1 after two commands?