<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 {
    int N;
    vector<vector<int>> dp[2];
    int md;
    void rec( int absent, int idx,  int lateConsec)
    {
        //cout<<absent<<" "<< idx<<" " <<lateConsec<<"\n";
        long long ans=0;
        if( idx== N)
        {
            ans= ( absent <=1 && (lateConsec<3))?1:0;
        }
        else
        {
            //3 values allowed( a, p, l)
            if( lateConsec <= 1)   //l
            {
                if( dp[absent][idx+1][lateConsec+1]== -1)
                    rec( absent, idx+1, lateConsec+ 1);
                ans= (ans*1ll + dp[absent][idx+1][lateConsec+1])%md;
            }
            if( absent ==0)  //a
            {
                if( dp[1][idx+1][0] == -1)
                    rec( 1, idx+1, 0);
                ans= (ans*1ll+ dp[1][idx+1][0])%md;
            }
            if( dp[absent][idx+1][0]== -1)
                rec(absent, idx+1, 0 );    //p
            ans= (ans*1ll + dp[absent][idx+1][0]) % md;
        }
        dp[absent][idx][lateConsec]= ans;
    }
public:
    int checkRecord(int n) {

        for( int j= 0; j<=1; j++)
        {
            dp[j].resize(n+1);
            for( int i=0; i<= n; i++)
            {
                dp[j][i]= vector<int>(4, -1);
            }
        }
        N= n;
        md= pow(10, 9)+ 7;
        rec( 0, 0, 0);
        return dp[0][0][0]; 
    }
};
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