<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:
  int rotatedDigits(int n) {
    vector<int> dp(n + 1);
    int res = 0;

    for (int i = 0; i <= n; i++) {
      if (i == 0 || i == 1 || i == 8) {
        dp[i] = 0;
      } else if (i == 2 || i == 5 || i == 6 || i == 9) {
        dp[i] = 1;
        res++;
      } else if (i == 3 || i == 4 || i == 7) {
        dp[i] = -1;
      } else {
        int remainder = i % 10;
        int quotient = i / 10;
        if (dp[remainder] == -1 || dp[quotient] == -1) {
          dp[i] = -1;
        } else if (dp[remainder] == 1 || dp[quotient] == 1) {
          dp[i] = 1;
          res++;
        } else {
          dp[i] = 0;
        }
      }
    }

    return res;
  }
};
8200