<p>A sequence is <strong>special</strong> if it consists of a <strong>positive</strong> number of <code>0</code>s, followed by a <strong>positive</strong> number of <code>1</code>s, then a <strong>positive</strong> number of <code>2</code>s.</p>

<ul>
	<li>For example, <code>[0,1,2]</code> and <code>[0,0,1,1,1,2]</code> are special.</li>
	<li>In contrast, <code>[2,1,0]</code>, <code>[1]</code>, and <code>[0,1,2,0]</code> are not special.</li>
</ul>

<p>Given an array <code>nums</code> (consisting of <strong>only</strong> integers <code>0</code>, <code>1</code>, and <code>2</code>), return<em> the <strong>number of different subsequences</strong> that are special</em>. Since the answer may be very large, <strong>return it modulo </strong><code>10<sup>9</sup> + 7</code>.</p>

<p>A <strong>subsequence</strong> of an array is a sequence that can be derived from the array by deleting some or no elements without changing the order of the remaining elements. Two subsequences are <strong>different</strong> if the <strong>set of indices</strong> chosen are different.</p>

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

<pre>
<strong>Input:</strong> nums = [0,1,2,2]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The special subsequences are bolded [<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>,2], [<strong><u>0</u></strong>,<strong><u>1</u></strong>,2,<strong><u>2</u></strong>], and [<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>,<strong><u>2</u></strong>].
</pre>

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

<pre>
<strong>Input:</strong> nums = [2,2,0,0]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There are no special subsequences in [2,2,0,0].
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [0,1,2,0,1,2]
<strong>Output:</strong> 7
<strong>Explanation:</strong> The special subsequences are bolded:
- [<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>,0,1,2]
- [<strong><u>0</u></strong>,<strong><u>1</u></strong>,2,0,1,<strong><u>2</u></strong>]
- [<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>,0,1,<strong><u>2</u></strong>]
- [<strong><u>0</u></strong>,<strong><u>1</u></strong>,2,0,<strong><u>1</u></strong>,<strong><u>2</u></strong>]
- [<strong><u>0</u></strong>,1,2,<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>]
- [<strong><u>0</u></strong>,1,2,0,<strong><u>1</u></strong>,<strong><u>2</u></strong>]
- [0,1,2,<strong><u>0</u></strong>,<strong><u>1</u></strong>,<strong><u>2</u></strong>]
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 2</code></li>
</ul>

class Solution:
    def countSpecialSubsequences(self, nums: List[int]) -> int:
        MOD = 10**9 + 7
        n = len(nums)
        dp = [[0, 0, 0] for _ in range(n + 1)]
        
        for i in range(n):
            for j in range(3):
                dp[i + 1][j] = dp[i][j]
            if nums[i] == 0:
                dp[i + 1][0] = (dp[i][0] * 2 + 1) % MOD
            elif nums[i] == 1:
                dp[i + 1][1] = (dp[i][1] * 2 + dp[i][0]) % MOD
            elif nums[i] == 2:
                dp[i + 1][2] = (dp[i][2] * 2 + dp[i][1]) % MOD
        
        return dp[n][2]
2006