<p>An integer <code>x</code> is a <strong>good</strong> if after rotating each digit individually by 180 degrees, we get a valid number that is different from <code>x</code>. Each digit must be rotated - we cannot choose to leave it alone.</p>

<p>A number is valid if each digit remains a digit after rotation. For example:</p>

<ul>
	<li><code>0</code>, <code>1</code>, and <code>8</code> rotate to themselves,</li>
	<li><code>2</code> and <code>5</code> rotate to each other (in this case they are rotated in a different direction, in other words, <code>2</code> or <code>5</code> gets mirrored),</li>
	<li><code>6</code> and <code>9</code> rotate to each other, and</li>
	<li>the rest of the numbers do not rotate to any other number and become invalid.</li>
</ul>

<p>Given an integer <code>n</code>, return <em>the number of <strong>good</strong> integers in the range </em><code>[1, n]</code>.</p>

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

<pre>
<strong>Input:</strong> n = 10
<strong>Output:</strong> 4
<strong>Explanation:</strong> There are four good numbers in the range [1, 10] : 2, 5, 6, 9.
Note that 1 and 10 are not good numbers, since they remain unchanged after rotating.
</pre>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 0
</pre>

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

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    bool isValid(string s) {
        bool hasDifferent = false;
        for (char c : s) {
            if (c == '3' || c == '4' || c == '7') {
                return false;
            }
            if (c == '2' || c == '5' || c == '6' || c == '9') {
                hasDifferent = true;
            }
        }
        return hasDifferent;
    }

    void generate(string s, int n, vector<char>& mp, int& count) {
        if (!s.empty() && stoi(s) <= n) {
            if (isValid(s)) {
                count++;
            }
        }
        if (s.size() >= to_string(n).size()) {
            return;
        }
        for (char c : mp) {
            if (s.empty() && c == '0') continue; // Skip leading zeros
            generate(s + c, n, mp, count);
        }
    }

    int rotatedDigits(int n) {
        vector<char> mp = {'0', '1', '2', '5', '6', '8', '9'};
        int count = 0;
        generate("", n, mp, count);
        return count;
    }
};
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