# Count Number of Special Subsequences Solution Leetcode United states 2021

A sequence is **special** if it consists of a **positive** number of `0`

s, followed by a **positive** number of `1`

s, then a **positive** number of `2`

s.

- For example,
`[0,1,2]`

and`[0,0,1,1,1,2]`

are special. - In contrast,
`[2,1,0]`

,`[1]`

, and`[0,1,2,0]`

are not special.

Given an array `nums`

(consisting of **only** integers `0`

, `1`

, and `2`

), return* the number of different subsequences that are special*. Since the answer may be very large,

**return it modulo**

`10`^{9} + 7

.A **subsequence** 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 **different** if the **set of indices** chosen are different.

**Example 1:**

Input:nums = [0,1,2,2]Output:3Explanation:The special subsequences are [0,1,2,2], [0,1,2,2], and [0,1,2,2].

**Example 2:**

Input:nums = [2,2,0,0]Output:0Explanation:There are no special subsequences in [2,2,0,0].

**Example 3:**

Input:nums = [0,1,2,0,1,2]Output:7Explanation:The special subsequences are: - [0,1,2,0,1,2] - [0,1,2,0,1,2] - [0,1,2,0,1,2] - [0,1,2,0,1,2] - [0,1,2,0,1,2] - [0,1,2,0,1,2] - [0,1,2,0,1,2]

**Constraints:**

`1 <= nums.length <= 10`

^{5}`0 <= nums[i] <= 2`