<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:
        s = str(n)
        N = len(s)
        res = 0
        def combo(a: int, b: int) -> int:
            ret = 1
            for i in range(b):
                ret *= (a - i)
            return ret
        for i in range(1, N):
            res += combo(10, i) - combo(9, i - 1)
        visited = [0] * 10 
        def dfs(cur: int):
            nonlocal res
            if cur >= N:
                res += 1
                return
            for i in range(10):
                if cur == 0 and i == 0: continue
                if visited[i]: continue
                if i < int(s[cur]):
                    res += combo(10 - (cur + 1), N - cur - 1)
                elif i == int(s[cur]): 
                    visited[i] = 1
                    dfs(cur + 1)
                    visited[i] = 0
        dfs(0)
        return res
31