# 1955. Count Number of Special Subsequences

https://leetcode.com/problems/count-number-of-special-subsequences

## Description

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** `109 + 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:** 3
**Explanation:** The special subsequences are bolded [**0**,**1**,**2**,2], [**0**,**1**,2,**2**], and [**0**,**1**,**2**,**2**].
```

**Example 2:**

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

**Example 3:**

```
**Input:** nums = [0,1,2,0,1,2]
**Output:** 7
**Explanation:** The special subsequences are bolded:
- [**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 <= 105`
* `0 <= nums[i] <= 2`

## ac

```java
```
