<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 {
    bool isValid(int n) {
        bool valid = false;
        while (n) {
            int d = n % 10;
            if (d == 3 || d == 4 || d == 7) {
                return false;
            }
            if (d == 2 || d == 5 || d == 6 || d == 9) {
                valid = true;
            }
            n /= 10;
        }
        return valid;
    }
public:
    // naive solution 
    int rotatedDigits1(int n) {
        int res = 0;
        for (int i = 1; i <= n; ++i) {
            if (isValid(i)) {
                ++res;
            }
        }
        return res; 
    }

    int rotatedDigits(int n) {
        vector<int> dp(n + 1);
        int res = 0;
        for (int i = 0; i <= n; ++i) {
            if (i < 10) {
                if (i == 0 || i == 1 || i == 8) {
                    dp[i] = 1;
                } else if (i == 2 || i == 5 || i == 6 || i == 9) {
                    dp[i] = 2;
                    ++res;
                }
            } else {
                int a = dp[i / 10], b = dp[i % 10];
                if (a == 1 && b == 1) {
                    dp[i] = 1;
                } else if (a >= 1 && b >= 1) {
                    dp[i] = 2;
                    ++res;
                }
            }
        }
        return res;
    }


};
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