<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 {
public:
    long long dp[11][1055][2][2][2];
    int rec(int idx, int mask, int rep, int ub, int lz, string num)
    {
        if (idx==num.size()) return rep;
        if (dp[idx][mask][rep][ub][lz]!=-1) return dp[idx][mask][rep][ub][lz];
        int low = 0, high = 9;
        if (ub) high = num[idx] - '0';
        int ways = 0;
        for (int i=low; i<=high; i++)
        {
            if (i==0)
            {
                if (lz==0)
                {
                    if (mask&(1<<i)) 
                    {
                        ways += rec(idx+1, mask | (1<<i), 1, ub&(i==high), lz&(i==0), num);
                    }
                    else ways += rec(idx+1, mask | (1<<i), rep, ub&(i==high), lz&(i==0), num);
                } 
                else 
                {
                    ways += rec(idx+1, mask , rep, ub&(i==high), lz&(i==0), num);
                }
            }
            else
            {
                if ((mask&(1<<i)))
                {
                    ways += rec(idx+1, mask | (1<<i), 1, ub&(i==high), 0, num);
                } 
                else ways += rec(idx+1, mask | (1<<i), rep, ub&(i==high), 0, num);
            }
        }
        return dp[idx][mask][rep][ub][lz] = ways; 
    }

    int numDupDigitsAtMostN(int n) {
        string num = to_string(n);
        memset(dp, -1, sizeof(dp));
        return rec(0, 0, 0, 1, 1, num);

    }
};
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