Problem:
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.

Sample Input 1

3

Sample Output 1

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.

Sample Input 2

4

Sample Output 2

230

Sample Input 3

100

Sample Output 3

388130742

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

Solution in Rust (1.15.1) (judge verdict: Accepted)

//! ----------------------------------------------
//! Framework <https://github.com/vain0x/procon>
//!
//! See the bottom of file for solution.
//! ----------------------------------------------

#![allow(unused_imports)]
#![allow(non_snake_case)]

use std::cell::RefCell;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::fmt::{Debug, Display, Formatter, Write as FmtWrite};
use std::io::{stderr, stdin, BufRead, Write};
use std::mem::{replace, swap};
use std::ops::*;
use std::rc::Rc;

/// Print values to standard error if debug mode.
#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), stderr());
            writeln!(err, "\x1B[33m{}\x1B[0m = {:?}", e, $e).unwrap()
        })*
    };
}

/// Read from standard input and parse each word.
/// - `read!(T, U, ..)` parses a line as a tuple of words.
/// - `read![[T]]` parses a line as an array of words.
/// - `read![..; N]` parses `N` lines, using `read!(..)` repeatedly.
#[allow(unused_macros)]
macro_rules! read {
    ([$t:ty] ; $n:expr) =>
        ((0..$n).map(|_| read!([$t])).collect::<Vec<_>>());
    ($($t:ty),+ ; $n:expr) =>
        ((0..$n).map(|_| read!($($t),+)).collect::<Vec<_>>());
    ([$t:ty]) =>
        (rl().split_whitespace().map(|w| w.parse().unwrap()).collect::<Vec<$t>>());
    ($($t:ty),*) => {{
        let buf = rl();
        let mut w = buf.split_whitespace();
        ($(w.next().unwrap().parse::<$t>().unwrap()),*)
    }};
}

/// Read a line from standard input.
#[allow(dead_code)]
fn rl() -> String {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();

    #[allow(deprecated)]
    buf.trim_right().to_owned()
}

// -----------------------------------------------
// Solution
// -----------------------------------------------

const P: i64 = 1_000_000_007;

fn decode(i: usize) -> char {
    match i {
        0 => ' ',
        1 => 'A',
        2 => 'C',
        3 => 'G',
        4 => 'T',
        _ => unreachable!(),
    }
}

fn is_banned(x: usize, y: usize, z: usize, w: usize) -> bool {
    match (decode(x), decode(y), decode(z), decode(w)) {
        ('A', 'G', _, 'C')
        | ('A', _, 'G', 'C')
        | (_, 'A', 'G', 'C')
        | (_, 'A', 'C', 'G')
        | (_, 'G', 'A', 'C') => true,
        _ => false,
    }
}

fn main() {
    let N = read!(usize);

    // dp[i][x][y][z] = 場合の数
    // 前から i 文字が確定済み
    // i-3, i-2, i-1 文字目がそれぞれ x, y, z

    let mut dp = vec![vec![vec![vec![0; 5]; 5]; 5]; N + 1];
    let mut ok = vec![vec![vec![vec![false; 5]; 5]; 5]; N + 1];

    dp[0][0][0][0] = 1_i64;
    ok[0][0][0][0] = true;

    for i in 0..N {
        for x in 0..5 {
            for y in 0..5 {
                for z in 0..5 {
                    if !ok[i][x][y][z] {
                        continue;
                    }

                    for w in 1..5 {
                        if is_banned(x, y, z, w) {
                            continue;
                        }

                        dp[i + 1][y][z][w] += dp[i][x][y][z];
                        ok[i + 1][y][z][w] = true;
                    }
                }
            }
        }

        for y in 0..5 {
            for z in 0..5 {
                for w in 0..5 {
                    dp[i + 1][y][z][w] %= P;
                }
            }
        }
    }

    debug!(dp, ok);

    let mut total = 0_i64;

    for x in 1..5 {
        for y in 1..5 {
            for z in 1..5 {
                if ok[N][x][y][z] {
                    total += dp[N][x][y][z];
                }
            }
        }
    }

    println!("{}", total % P)
}