<p>An attendance record for a student can be represented as a string where each character signifies whether the student was absent, late, or present on that day. The record only contains the following three characters:</p>

<ul>
	<li><code>&#39;A&#39;</code>: Absent.</li>
	<li><code>&#39;L&#39;</code>: Late.</li>
	<li><code>&#39;P&#39;</code>: Present.</li>
</ul>

<p>Any student is eligible for an attendance award if they meet <strong>both</strong> of the following criteria:</p>

<ul>
	<li>The student was absent (<code>&#39;A&#39;</code>) for <strong>strictly</strong> fewer than 2 days <strong>total</strong>.</li>
	<li>The student was <strong>never</strong> late (<code>&#39;L&#39;</code>) for 3 or more <strong>consecutive</strong> days.</li>
</ul>

<p>Given an integer <code>n</code>, return <em>the <strong>number</strong> of possible attendance records of length</em> <code>n</code><em> that make a student eligible for an attendance award. The answer may be very large, so return it <strong>modulo</strong> </em><code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 8
<strong>Explanation:</strong> There are 8 records with length 2 that are eligible for an award:
&quot;PP&quot;, &quot;AP&quot;, &quot;PA&quot;, &quot;LP&quot;, &quot;PL&quot;, &quot;AL&quot;, &quot;LA&quot;, &quot;LL&quot;
Only &quot;AA&quot; is not eligible because there are 2 absences (there need to be fewer than 2).
</pre>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 3
</pre>

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

<pre>
<strong>Input:</strong> n = 10101
<strong>Output:</strong> 183236316
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
    const int MAX_ABSENT = 1;
    const int MAX_LATE = 2;
    const int MOD = 1000000007;

    int countCombinations(int n, int absence, int late) {
        if (absence > MAX_ABSENT || late > MAX_LATE) {
            return 0;
        }

        if (n == 0) {
            return 1;
        }

        // Add "P", absence is the same, reset late
        int count = countCombinations(n - 1, absence, 0);
        // Add "A", increment absence, reset late
        count = (count + countCombinations(n - 1, absence + 1, 0)) % MOD;
        // Add "L", absence is the same, increment consecutive late
        count = (count + countCombinations(n - 1, absence, late + 1)) % MOD;

        return count;
    }
    
public:
    int checkRecord(int n) {
        // return countCombinations(n, 0, 0);

        vector<vector<vector<int>>> previous(1, vector<vector<int>>(2, vector<int>(3, 0)));
        vector<vector<vector<int>>> current(1, vector<vector<int>>(2, vector<int>(3, 0)));

        // Seed base case
        previous[0][0][0] = 1;

        for (int len = 0; len < n; len++) {
            for (int absence = 0; absence <= MAX_ABSENT; absence++) {
                for (int late = 0; late <= MAX_LATE; late++) {
                    // Select "P"
                    current[0][absence][0] = (current[0][absence][0] + previous[0][absence][late]) % MOD;
                    // Select "A"
                    if (absence < MAX_ABSENT) {
                        current[0][absence + 1][0] = (current[0][absence + 1][0] + previous[0][absence][late]) % MOD;
                    }
                    // Select "L"
                    if (late < MAX_LATE) {
                        current[0][absence][late + 1] = (current[0][absence][late + 1] + previous[0][absence][late]) % MOD;
                    }
                }
            }

            previous = current;
            current = vector<vector<vector<int>>>(1, vector<vector<int>>(2, vector<int>(3, 0)));
        }

        int count  = 0;
        for (int absence = 0; absence <= MAX_ABSENT; absence++) {
            for (int late  = 0; late <= MAX_LATE; late++) {
                count = (count + previous[0][absence][late]) % MOD;
            }
        }

        return count;
    }
};
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