<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 {
    long long M = 1000000007;
public:
    long long dp(int idx, int absent, int late, auto& memo){

        if(absent==0)return 0;
        if(late==0)return 0;

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

        if(memo[idx][absent][late]!=-1)return memo[idx][absent][late];

        long long ans = 0;
        ans = dp(idx-1,absent,3,memo);
        ans = (ans + dp(idx-1, absent-1, 3, memo))%1000000007;
        ans = (ans + dp(idx-1, absent, late-1, memo))%1000000007;

        return memo[idx][absent][late] = ans;
    }   

    int checkRecord(int n) {
        
        vector<vector<vector<long long>>> memo(n+1,vector<vector<long long>>(3,vector<long long>(4,0))); 

        memo[1][2][3] = memo[1][1][3] = memo[1][2][2] = 1;
        for(int i=2;i<=n;i+=1){
            for(int j=1;j<=2;j+=1){
                for(int k=1;k<=3;k+=1){
                    if(k==1){
                        memo[i][j][k] = memo[i-1][j][2];
                    }else if(k==2){
                        memo[i][j][k] = memo[i-1][j][3];
                    }else if(k==3){

                        if(j==2){
                            memo[i][j][k] = ((memo[i-1][2][3] + memo[i-1][2][2])%M + memo[i-1][2][1])%M;
                        }else{
                            memo[i][j][k] = ((memo[i-1][1][3] + memo[i-1][1][2])%M + memo[i-1][1][1])%M;
                            memo[i][j][k] = (((memo[i][j][k] + memo[i-1][2][3])%M+memo[i-1][2][2])%M +memo[i-1][2][1])%M;
                        }
                        

                        // if(j==1){
                        //     memo[i][j][k] = ((memo[i][j][k] + memo[i-1][2][3])%M+memo[i-1][1][3])%M;
                        // }
                        /*
                        
                        */
                        
                    }

                    // cout<<i<<" "<<j<<" "<<k<<" "<<memo[i][j][k]<<endl;
                }
            }
        }

        long long sum = 0;
        for(int ab=1;ab<=2;ab+=1){
            for(int lt=1;lt<=3;lt+=1){
                sum = (sum + memo[n][ab][lt])%M;
            }
        }
        return sum;

    }
};

/*
n, 2, 3
PP-
PA--
PL- 
AP--
AL
LP-
LA--
LL-


*/
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