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:
'A'
: Absent.'L'
: Late.'P'
: Present.
Any student is eligible for an attendance award if they meet both of the following criteria:
 The student was absent (
'A'
) for strictly fewer than 2 days total.  The student was never late (
'L'
) for 3 or more consecutive days.
Given an integer n
, return the number of possible attendance records of length n
that make a student eligible for an attendance award. The answer may be very large, so return it modulo 10^{9} + 7
.
Example 1:
Input: n = 2
Output: 8
Explanation: There are 8 records with length 2 that are eligible for an award:
"PP", "AP", "PA", "LP", "PL", "AL", "LA", "LL"
Only "AA" is not eligible because there are 2 absences (there need to be fewer than 2).
Example 2:
Input: n = 1
Output: 3
Example 3:
Input: n = 10101
Output: 183236316
Constraints:
1 <= n <= 10^{5}

