<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>

enum Goodness{
    GOOD, BAD, NEUTRAL
};

Goodness rateGoodness(uint8_t n){
    switch(n){
        case 0:
        case 1:
        case 8:
            return NEUTRAL;
        
        case 2:
        case 5:
        case 6:
        case 9:
            return GOOD;
        
        default:
            return BAD;
    }
}

class NumberChain {
    private:
        vector<int> numberChain;
    public:
        NumberChain() : numberChain(1){
            numberChain[0] = 1;
        }

        void increase(){
            int level = 0;
            bool keepGoing = true;

            while(keepGoing){
                keepGoing = false;
                numberChain[level]++;
                if(numberChain[level]==10){
                    numberChain[level] = 0;
                    keepGoing = true;
                    level++;
                    if(level >= numberChain.size()){
                        numberChain.push_back(0);
                    }
                }
            }
        }

        bool isGood(){
            bool anyGood = false;

            for(size_t i = 0;i<numberChain.size();i++){
                Goodness g(rateGoodness(numberChain[i]));
                
                switch(g){
                    case GOOD:
                        anyGood = true;
                        break;
                    case BAD:
                        return false;
                        break;
                }
            }

            return anyGood;
        }

};

class Solution {
public:
    int rotatedDigits(int n) {
        uint16_t counter = 0;
        NumberChain nc;
        for(int i=1;i<=n;i++){
            if(nc.isGood()) counter++;
            nc.increase();
        }

        return counter;
    }
};
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