Problem Arrangement

An assignment is impossible if $N<3$ or either type is absent. Binary search a candidate width $D$, and sort each type separately. Let a type have minimum $a$ and maximum $b$. If $b-a\le D$, leave the entire type in its outer division. Otherwise consider two choices. To leave $b$ outside, every value below $b-D$ is forced into Div.2. To leave $a$ outside, every value above $a+D$ is forced into Div.2. These choices are exhaustive. A feasible Div.2 cannot leave both extremes outside. If it contains $a$ but not $b$, the outer division containing $b$ forces the lower prefix. If it contains $b$ but not $a$, it forces the upper suffix. If it contains both, its own width would exceed $D$, which is impossible. Try all four direction combinations for E and H. If the union of forced values has width at most $D$, place it in Div.2 and leave all other values in their respective outer divisions. Each forced set excludes the opposite extreme, so both outer divisions remain nonempty. If both forced sets are empty, move one item to Div.2 while leaving the outer divisions nonempty; this is possible because $N\ge3$ and both types exist. Subtask 1 enumerates the two legal division choices of every item in $O(2^N N)$ time. The full solution sorts once and finds forced-set boundaries by binary search, taking $O(N\log N+\log V\log N)$ time and $O(N)$ memory, where $V$ is the difficulty range. Values and differences are at most $10^9$, safely within signed 64-bit integers. Solution written by GPT6.1