Increasing Triplet Subsequence

You are given an array of integers. Your task is to determine whether there exists a strictly increasing triplet in the array. More formally, you need to check if there exist indices \( i, j, k \) with \( i < j < k \) such that:

\( nums[i] < nums[j] < nums[k] \)

If such a triplet exists, output True; otherwise, output False.

Example

• For the input array [1, 2, 3, 4, 5], the output should be True because \(1 < 2 < 3\) (among many other triplets) is a valid increasing triplet.
• For the input array [5, 4, 3, 2, 1], the output should be False.

inputFormat

The first line contains an integer \( n \) representing the number of elements in the array. The second line contains \( n \) space-separated integers representing the elements of the array.

outputFormat

Output a single line containing either True or False depending on whether there exists an increasing triplet subsequence.

5
1 2 3 4 5

True