Maximum Width of an Equal-Height Fence

# Maximum Width of an Equal-Height Fence You are given the heights of wooden planks in `planks`. Each original plank has width `1`. Build a fence whose resulting planks all have the same height. A resulting plank may be either: - One original plank used unchanged; or - A single plank formed by joining exactly two different original planks, with height equal to the sum of their heights and width `1`. Each original plank can be used at most once, and unused planks may be discarded. Return the maximum possible fence width. ### Function `int maximumWidth(vector<int>& planks)` ### Example 1 **Input:** `planks = [2, 2, 3, 3, 5, 5]` **Output:** `4` **Explanation:** Use the two original planks of height `5`, and form two more height-`5` planks by pairing a `2` with a `3` each time. The four resulting planks have total width `4`. ### Example 2 **Input:** `planks = [4, 4, 4, 8]` **Output:** `3` **Explanation:** Use the three original height-`4` planks and discard the `8`. At height `8`, the original `8` plus one pair of `4`s would give only width `2`. ### Constraints - `1 <= planks.length <= 1000` - `1 <= planks[i] <= 1000000000` ### Clarifications - Different original planks means different indices; equal heights may be paired. - Joining two planks creates one unit of fence width, not two. - A joined plank cannot be joined again: each resulting plank uses exactly one or two originals. - You may choose any common height and do not need to use every original plank. ### What a Strong Answer Covers - Maximizing the number of equal-height resulting planks without reusing originals. - Combining unchanged planks and valid pairs, including pairs of equal heights. - Supporting large heights without scanning every possible integer height.