2376\. Count Special Integers

Hard

We call a positive integer **special** if all of its digits are **distinct**.

Given a **positive** integer `n`, return _the number of special integers that belong to the interval_ `[1, n]`.

**Example 1:**

**Input:** n = 20

**Output:** 19

**Explanation:** All the integers from 1 to 20, except 11, are special. Thus, there are 19 special integers. 

**Example 2:**

**Input:** n = 5

**Output:** 5

**Explanation:** All the integers from 1 to 5 are special. 

**Example 3:**

**Input:** n = 135

**Output:** 110

**Explanation:** There are 110 integers from 1 to 135 that are special.

Some of the integers that are not special are: 22, 114, and 131.

**Constraints:**

*   <code>1 <= n <= 2 * 10<sup>9</sup></code>