trionic-array-ii

You are given an integer array nums of length n.

A trionic subarray is a contiguous subarray nums[l...r] (with 0 <= l < r < n) for which there exist indices l < p < q < r such that:

• nums[l...p] is strictly increasing,


• nums[p...q] is strictly decreasing,


• nums[q...r] is strictly increasing.

Return the maximum sum of any trionic subarray in nums.

Example 1:

Input: nums = [0,-2,-1,-3,0,2,-1]

Output: -4

Explanation:

Pick l = 1, p = 2, q = 3, r = 5:

• nums[l...p] = nums[1...2] = [-2, -1] is strictly increasing (-2 < -1).


• nums[p...q] = nums[2...3] = [-1, -3] is strictly decreasing (-1 > -3)


• nums[q...r] = nums[3...5] = [-3, 0, 2] is strictly increasing (-3 < 0 < 2).


• Sum = (-2) + (-1) + (-3) + 0 + 2 = -4.

Example 2:

Input: nums = [1,4,2,7]

Output: 14

Explanation:

Pick l = 0, p = 1, q = 2, r = 3:

• nums[l...p] = nums[0...1] = [1, 4] is strictly increasing (1 < 4).


• nums[p...q] = nums[1...2] = [4, 2] is strictly decreasing (4 > 2).


• nums[q...r] = nums[2...3] = [2, 7] is strictly increasing (2 < 7).


• Sum = 1 + 4 + 2 + 7 = 14.

Constraints:

• 4 <= n = nums.length <= 105


• -109 <= nums[i] <= 109


• It is guaranteed that at least one trionic subarray exists.