<p>We call a positive integer <strong>special</strong> if all of its digits are <strong>distinct</strong>.</p>

<p>Given a <strong>positive</strong> integer <code>n</code>, return <em>the number of special integers that belong to the interval </em><code>[1, n]</code>.</p>

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

<pre>
<strong>Input:</strong> n = 20
<strong>Output:</strong> 19
<strong>Explanation:</strong> All the integers from 1 to 20, except 11, are special. Thus, there are 19 special integers.
</pre>

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

<pre>
<strong>Input:</strong> n = 5
<strong>Output:</strong> 5
<strong>Explanation:</strong> All the integers from 1 to 5 are special.
</pre>

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

<pre>
<strong>Input:</strong> n = 135
<strong>Output:</strong> 110
<strong>Explanation:</strong> There are 110 integers from 1 to 135 that are special.
Some of the integers that are not special are: 22, 114, and 131.</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 2 * 10<sup>9</sup></code></li>
</ul>

class Solution:
    def countSpecialNumbers(self, n: int) -> int:
        def count_permutations(m, k):
            return math.perm(m, k)

        def count_special_numbers_with_length(length):
            if length == 1:
                return 9
            return 9 * count_permutations(9, length - 1)

        # Count special numbers with less digits than n
        digits = list(str(n))
        num_digits = len(digits)
        count = sum(count_special_numbers_with_length(i) for i in range(1, num_digits))

        # Count special numbers with the same number of digits as n
        used = set()
        for i, digit in enumerate(digits):
            curr_digit = int(digit)
            for d in range(0 if i > 0 else 1, curr_digit):
                if d not in used:
                    count += count_permutations(9 - i, num_digits - i - 1)
            if curr_digit in used:
                break
            used.add(curr_digit)
        else:
            count += 1  # n itself is special

        return count
    
34