<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>

const int modulo = 1000000007;

struct Count {
    int EndsWithZeroL;
    int EndsWithOneL;
    int EndsWithTwoL;

    Count( int zero, int one, int two ) : EndsWithZeroL( zero ), EndsWithOneL( one ), EndsWithTwoL( two ) {}

    void MoveForward() {
        const int64_t sum =  static_cast<int64_t>(EndsWithZeroL) + EndsWithOneL + EndsWithTwoL;
        EndsWithTwoL = EndsWithOneL;
        EndsWithOneL = EndsWithZeroL;
        EndsWithZeroL = static_cast<int>( sum % modulo );
    }

    int Sum() {
        return ( (EndsWithZeroL + EndsWithOneL) % modulo + EndsWithTwoL) % modulo;
    }
};

class Solution {
public:
    int checkRecord(int n)
    {
        if( n == 1 ) return 3;

        vector<Count> cache;
        cache.push_back( Count( 1, 1, 0 ) );
        for( int i = 0; i < n - 1; i++ ) {
            Count tmp = cache.back();
            tmp.MoveForward();
            cache.push_back( tmp );
        }
        const int result1 = cache.back().Sum();
        int result = 0;
        for( int i = 0; i < n / 2; i++ ) {
            const int64_t totalCurrent = static_cast<int64_t>( i == 0 ? 1 : cache[i-1].Sum() ) * cache[n-i-2].Sum();
            const int current = static_cast<int>( totalCurrent % modulo );
            result = (result + current) % modulo;
        }
        result *= 2;
        result %= modulo;
        if( n % 2 == 1 ) {
            int64_t totalCurrent = cache[n / 2 - 1].Sum();
            totalCurrent *= totalCurrent;
            const int current = static_cast<int>( totalCurrent % modulo );
            result = (result + current) % modulo;
        }
        return (result1 + result) % modulo;
    }
};
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