Given an integer array `nums`, return `true` if there exists a triple of indices `(i, j, k)` such that `i < j < k` and `nums[i] < nums[j] < nums[k]`. If no such indices exists, return `false`.

Example 1:

    Input: nums = [1,2,3,4,5]
    Output: true
    Explanation: Any triplet where i < j < k is valid.

Example 2:

    Input: nums = [5,4,3,2,1]
    Output: false
    Explanation: No triplet exists.

Example 3:

    Input: nums = [2,1,5,0,4,6]
    Output: true
    Explanation: The triplet (3, 4, 5) is valid because nums[3] == 0 < nums[4] == 4 < nums[5] == 6.

Constraints:

- `1 <= nums.length <= 5 * 105`
- `-231 <= nums[i] <= 231 - 1`

Follow up: Could you implement a solution that runs in `O(n)` time complexity and `O(1)` space complexity?