Maximum Score of a Good Subarray

Find the maximum value of min(nums[i..j]) * (j - i + 1) over all subarrays [i, j] that contain index k — i.e., the largest "area" under the array-as-histogram subject to including bar k. The core challenge is to efficiently maximize this min×length product (n up to 1e5), typically solved with a linear two-pointer expansion or monotonic-stack pattern.