<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:
    long modulo = 1000000007;
    int checkRecord(int n) {
        if(n < 4) return n == 1 ? 3 : (n == 2 ? 8 : 19);
        vector<long> dp(n + 1, 0);
        vector<long> dpwoa(n + 1, 0);
        dp[1] = 3;
        dpwoa[1] = 2;
        dp[2] = 8;
        dpwoa[2] = 4;
        dp[3] = 19;
        dpwoa[3] = 7;
        dp[4] = 43;
        dpwoa[4] = 13;
        for(int i = 5; i <= n; i++)
        {
            dp[i] = ((2*dp[i-1]) + dpwoa[i-1] - dp[i-4] - dpwoa[i-4]) % modulo;
            dpwoa[i] = ((2*dpwoa[i-1]) - dpwoa[i-4]) % modulo;
            //cout << dp[i] << " : "<< dpwoa[i] << endl;
        }
        return dp.back() < 0 ? dp.back() + modulo : dp.back();
    }
};

// 0 2 4 7

// 0 3 8 19 43 94 200 418 861 1756

// 2 3 5 8 12 18 25 31

42709