<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 {
public:
    int checkRecord(int n) {
        // Ending in absent/present
        // Ending in one late
        // Ending in 2 lates 
        int MOD = 1000000007; 
        vector<vector<long long>> noAbsence (n); 
        noAbsence[0] = {1, 1, 0}; 
        vector<vector<long long>> oneAbsence (n); 
        oneAbsence[0] = {1, 0, 0}; 
        for(int i = 1; i < n; i++) {

            noAbsence[i] = {
                (noAbsence[i - 1][0] + noAbsence[i - 1][1] + noAbsence[i - 1][2]) % MOD, 
                noAbsence[i - 1][0], 
                noAbsence[i - 1][1]
            }; 
            
            oneAbsence[i] = {
                (noAbsence[i - 1][0] + noAbsence[i - 1][1] + noAbsence[i - 1][2] + oneAbsence[i - 1][0] + oneAbsence[i - 1][1] + oneAbsence[i - 1][2]) % MOD,
                oneAbsence[i - 1][0],
                oneAbsence[i - 1][1]
            }; 

        }

        return (
            noAbsence[n - 1][0] + 
            noAbsence[n - 1][1] + 
            noAbsence[n - 1][2] + 
            oneAbsence[n - 1][0] + 
            oneAbsence[n - 1][1] +
            oneAbsence[n - 1][2]
        ) % MOD; 
    }
};
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