Hidden Permutation

A permutation of length $N$ is an array of $N$ integers such that every integer between $1$ and $N$ (inclusive) appears in it exactly once. Chef creates a set from a permutation $(P_1, P_2, \dots, P_N)$ of length $N$, as follows: - Initially Chef takes a empty set $S=\phi$, and then for every index $i\;(1\le i \le N)$, Chef insert a pair of integers $(l_i, r_i)$ into $S$, where $1\le l_i \le r_i