<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. You have to partition the array into one or more <strong>contiguous</strong> subarrays.</p>

<p>We call a partition of the array <strong>valid</strong> if each of the obtained subarrays satisfies <strong>one</strong> of the following conditions:</p>

<ol>
	<li>The subarray consists of <strong>exactly</strong> <code>2,</code> equal elements. For example, the subarray <code>[2,2]</code> is good.</li>
	<li>The subarray consists of <strong>exactly</strong> <code>3,</code> equal elements. For example, the subarray <code>[4,4,4]</code> is good.</li>
	<li>The subarray consists of <strong>exactly</strong> <code>3</code> consecutive increasing elements, that is, the difference between adjacent elements is <code>1</code>. For example, the subarray <code>[3,4,5]</code> is good, but the subarray <code>[1,3,5]</code> is not.</li>
</ol>

<p>Return <code>true</code><em> if the array has <strong>at least</strong> one valid partition</em>. Otherwise, return <code>false</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [4,4,4,5,6]
<strong>Output:</strong> true
<strong>Explanation:</strong> The array can be partitioned into the subarrays [4,4] and [4,5,6].
This partition is valid, so we return true.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,1,1,2]
<strong>Output:</strong> false
<strong>Explanation:</strong> There is no valid partition for this array.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
</ul>

class Solution:
    def validPartition(self, nums: List[int]) -> bool:
        """
        You are given a 0-indexed integer array nums. You have to partition the array into one or more contiguous subarrays.

        We call a partition of the array valid if each of the obtained subarrays satisfies one of the following conditions:

        1. The subarray consists of exactly 2 equal elements. For example, the subarray [2,2] is good.
        2. The subarray consists of exactly 3 equal elements. For example, the subarray [4,4,4] is good.
        3. The subarray consists of exactly 3 consecutive increasing elements, that is, the difference between adjacent elements is 1. For example, the subarray [3,4,5] is good, but the subarray [1,3,5] is not.

        Return true if the array has at least one valid partition. Otherwise, return false.



        Example 1:

        Input: nums = [4,4,4,5,6]
        Output: true
        Explanation: The array can be partitioned into the subarrays [4,4] and [4,5,6].
        This partition is valid, so we return true.


        Example 2:

        Input: nums = [1,1,1,2]
        Output: false
        Explanation: There is no valid partition for this array.



        Constraints:

        * 2 <= nums.length <= 10^5
        * 1 <= nums[i] <= 10^6
        """
        n = len(nums)
        dp = [False] * (n + 1)
        dp[n] = True
        for i in range(n - 1, -1, -1):
            if i + 2 <= n and nums[i] == nums[i + 1]:
                dp[i] = dp[i] or dp[i + 2]
            if i + 3 <= n and nums[i] == nums[i + 1] == nums[i + 2]:
                dp[i] = dp[i] or dp[i + 3]
            if i + 3 <= n and nums[i] + 1 == nums[i + 1] and nums[i + 1] + 1 == nums[i + 2]:
                dp[i] = dp[i] or dp[i + 3]
        return dp[0]

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