Count Bowl Subarrays

Count subarrays of length >= 3 where the smaller endpoint is strictly greater than every interior element — equivalently, count pairs (i, j) with j - i >= 2 and max(nums[i+1..j-1]) < min(nums[i], nums[j]). The challenge is to compute this for n up to 1e5 efficiently by exploiting monotonic/next-greater relationships rather than checking all pairs.