Igzi and Burly Array

Chef's friend Igzi is often at the coding gym, working out his mind muscles. When he is there, he asks Chef to guard his most prized posession: a sequence $A_1, A_2, \ldots, A_N$. Initially, for each $i$ ($1 \le i \le N$), $A_i = i$ held. However, Chef sometimes gets bored and starts playing with the sequence. Since $N$ can be very large, Chef has a lot of fun with it and he would like to share it