Given an integer array nums, determine if there exists at least one valid partition of the array.

A partition is considered valid if the entire array can be divided into one or more contiguous subarrays such that every subarray satisfies at least one of the following conditions:

1. The subarray consists of exactly $2$ equal elements (for example, [x, x]).

2. The subarray consists of exactly $3$ equal elements (for example, [x, x, x]).

3. The subarray consists of exactly $3$ consecutive increasing elements, where the difference between adjacent elements is equal to $1$ (for example, [x, x + 1, x + 2]).

Return true if nums has at least one valid partition, or false otherwise.

Constraints:

• $2 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^6$

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