3802. Number of Ways to Paint Sheets

Sort limit and use binary search (lower_bound) to compute num_ge(t), the number of colors with limit >= t.

For a split x, count ordered pairs (i, j) with i != j as num_ge(x) * num_ge(n - x) - num_ge(max(x, n - x)).

Note that num_ge(x) and num_ge(n - x) change only when x crosses 1, n - 1, L + 1, or n - L for some L in limit.

Collect all such critical x values, sort and deduplicate them, and treat the answer as constant between consecutive values.