Score : $400$ points

Problem Statement

You are given an integer $N$. Find the number of strings of length $N$ that satisfy the following conditions, modulo $10^9+7$:

• The string does not contain characters other than A, C, G and T.
• The string does not contain AGC as a substring.
• The condition above cannot be violated by swapping two adjacent characters once.

Notes

A substring of a string $T$ is a string obtained by removing zero or more characters from the beginning and the end of $T$.

For example, the substrings of ATCODER include TCO, AT, CODER, ATCODER and `` (the empty string), but not AC.

Constraints

• $3 \leq N \leq 100$

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the number of strings of length $N$ that satisfy the following conditions, modulo $10^9+7$.

3

61

There are $4^3 = 64$ strings of length $3$ that do not contain characters other than A, C, G and T. Among them, only AGC, ACG and GAC violate the condition, so the answer is $64 - 3 = 61$.

4

230

100

388130742

Be sure to print the number of strings modulo $10^9+7$.