<p>Given an integer <code>n</code>, return <em>the number of positive integers in the range </em><code>[1, n]</code><em> that have <strong>at least one</strong> repeated digit</em>.</p>

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

<pre>
<strong>Input:</strong> n = 20
<strong>Output:</strong> 1
<strong>Explanation:</strong> The only positive number (&lt;= 20) with at least 1 repeated digit is 11.
</pre>

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

<pre>
<strong>Input:</strong> n = 100
<strong>Output:</strong> 10
<strong>Explanation:</strong> The positive numbers (&lt;= 100) with atleast 1 repeated digit are 11, 22, 33, 44, 55, 66, 77, 88, 99, and 100.
</pre>

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

<pre>
<strong>Input:</strong> n = 1000
<strong>Output:</strong> 262
</pre>

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

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

class Solution:
    def numDupDigitsAtMostN(self, n: int) -> int:
        # Digit dp + bitmask
        digits = []
        num = n
        while(num > 0):
            digits.append(num % 10)
            num //= 10
        digits.reverse()
    

        # dp(i): number of special elements (refer to 2376 problem)
        # that have been constructed up until index i
        @cache
        def dp(i, tight, leadingZero, usedDigitMask):
            if i == len(digits):
                return 1
            
            ans = 0
            maxDigit = digits[i] if tight else 9
            for d in range(maxDigit + 1):
                if (usedDigitMask >> d) & 1:
                    continue
                nextLeadingZero = leadingZero and d == 0
                nextUsedDigitMask = usedDigitMask 
                nextTight = (tight and d == maxDigit)
                if not nextLeadingZero:
                    nextUsedDigitMask = usedDigitMask | (1 << d)
                ans += dp(i + 1, nextTight, nextLeadingZero, nextUsedDigitMask)
            return ans
        
        totalSpecials = dp(0, True, True, 0) - 1 # 1 for cases = 0
        print(totalSpecials)
        ans = n - totalSpecials
        return ans
22100