You are given a 0-indexed array nums of integers.
A triplet of indices (i, j, k) is a mountain if:
i < j < knums[i] < nums[j] and nums[k] < nums[j]Return the minimum possible sum of a mountain triplet of nums. If no such triplet exists, return -1.
\n
Example 1:
\n\n\nInput: nums = [8,6,1,5,3]\nOutput: 9\nExplanation: Triplet (2, 3, 4) is a mountain triplet of sum 9 since: \n- 2 < 3 < 4\n- nums[2] < nums[3] and nums[4] < nums[3]\nAnd the sum of this triplet is nums[2] + nums[3] + nums[4] = 9. It can be shown that there are no mountain triplets with a sum of less than 9.\n\n\n
Example 2:
\n\n\nInput: nums = [5,4,8,7,10,2]\nOutput: 13\nExplanation: Triplet (1, 3, 5) is a mountain triplet of sum 13 since: \n- 1 < 3 < 5\n- nums[1] < nums[3] and nums[5] < nums[3]\nAnd the sum of this triplet is nums[1] + nums[3] + nums[5] = 13. It can be shown that there are no mountain triplets with a sum of less than 13.\n\n\n
Example 3:
\n\n\nInput: nums = [6,5,4,3,4,5]\nOutput: -1\nExplanation: It can be shown that there are no mountain triplets in nums.\n\n\n
\n
Constraints:
\n\n3 <= nums.length <= 1051 <= nums[i] <= 108j, i will be the smallest integer to the left of j, and k the largest integer to the right of j.",
"To find i and k, preprocess the prefix minimum array prefix_min[i] = min(nums[0], nums[1], ..., nums[i]), and the suffix minimum array suffix_min[i] = min(nums[i], nums[i + 1], ..., nums[i - 1])."
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