Chef and Reordering

There are $N$ cells (numbered $1$ through $N$). Initially, each cell contains a single Chef. You are given $Q$ pairs of cell ranges $[L_1, R_1], [L_2, R_2], \ldots, [L_Q, R_Q]$. Consider a sequence of integers $a_1, a_2, \ldots, a_N$, where $1 \le a_i \le N$ for each valid $i$. For each $k$ from $1$ to $Q$, the following process is performed: - For each $i$ ($L_k \le i \le R_k$), the Chef from