Problem:
Score : 400 points

Problem Statement

We have a board with a 2 \times N grid.
Snuke covered the board with N dominoes without overlaps.
Here, a domino can cover a 1 \times 2 or 2 \times 1 square.

Then, Snuke decided to paint these dominoes using three colors: red, cyan and green.
Two dominoes that are adjacent by side should be painted by different colors.
Here, it is not always necessary to use all three colors.

Find the number of such ways to paint the dominoes, modulo 1000000007.

The arrangement of the dominoes is given to you as two strings S_1 and S_2 in the following manner:

Each domino is represented by a different English letter (lowercase or uppercase).

The j-th character in S_i represents the domino that occupies the square at the i-th row from the top and j-th column from the left.

Constraints

1 \leq N \leq 52

|S_1| = |S_2| = N

S_1 and S_2 consist of lowercase and uppercase English letters.

S_1 and S_2 represent a valid arrangement of dominoes.

Input

Input is given from Standard Input in the following format:

N
S_1
S_2

Output

Print the number of such ways to paint the dominoes, modulo 1000000007.

Sample Input 1

3
aab
ccb

Sample Output 1

6

There are six ways as shown below:

Sample Input 2

1
Z
Z

Sample Output 2

3

Note that it is not always necessary to use all the colors.

Sample Input 3

52
RvvttdWIyyPPQFFZZssffEEkkaSSDKqcibbeYrhAljCCGGJppHHn
RLLwwdWIxxNNQUUXXVVMMooBBaggDKqcimmeYrhAljOOTTJuuzzn

Sample Output 3

958681902

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

//! https://github.com/hatoo/competitive-rust-snippets
//!
//! MIT License
//!
//! Copyright (c) 2018 hatoo
//!
//! Permission is hereby granted, free of charge, to any person obtaining a copy
//! of this software and associated documentation files (the "Software"), to deal
//! in the Software without restriction, including without limitation the rights
//! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
//! copies of the Software, and to permit persons to whom the Software is
//! furnished to do so, subject to the following conditions:
//!
//! The above copyright notice and this permission notice shall be included in all
//! copies or substantial portions of the Software.
//!
//! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
//! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
//! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
//! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
//! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
//! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
//! SOFTWARE.
#![allow(unused_imports, unused_attributes, unused_macros, dead_code)]
use std::cmp::{max, min, Ordering};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::{stdin, stdout, BufWriter, Write};
use std::iter::FromIterator;
#[macro_export]
macro_rules !get {(@inner [$src :expr ] chars ) =>{{let mut buf =String ::new () ;$src .read_line (&mut buf ) .unwrap () ;buf .trim () .chars () .collect ::<Vec <char >>() } } ;(@inner [$src :expr ] usize1 ) =>{{get !(@inner [$src ] usize ) -1 } } ;(@inner [$src :expr ] [usize1 ] ) =>{{get !(@inner [$src ] [usize ] ) .into_iter () .map (|v |v -1 ) .collect ::<Vec <usize >>() } } ;(@inner [$src :expr ] [[usize1 ] ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] [usize1 ] ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [usize1 ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] [usize1 ] ) ) .flatten () .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [[chars ] ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] chars ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [chars ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] chars ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [($($tt :tt ) ,*) ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] ($($tt ) ,*) ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] ($($tt :tt ) ,*) ) =>{{let mut buf :String =String ::new () ;$src .read_line (&mut buf ) .unwrap () ;let mut iter =buf .split_whitespace () ;($(get !(@inner_elem_parse [$tt ] iter .next () .unwrap () ) ,) *) } } ;(@inner [$src :expr ] [$t :ty ] ) =>{{let mut buf =String ::new () ;$src .read_line (&mut buf ) .unwrap () ;buf .trim () .split_whitespace () .map (|t |t .parse ::<$t >() .unwrap () ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [[$t :ty ] ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] [$t ] ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [$t :ty ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] [$t ] ) ) .flatten () .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] $t :ty ) =>{{let mut buf =String ::new () ;$src .read_line (&mut buf ) .unwrap () ;buf .trim () .split_whitespace () .next () .unwrap () .parse ::<$t >() .unwrap () } } ;(@inner_elem_parse [usize1 ] $elem :expr ) =>{{get !(@inner_elem_parse [usize ] $elem ) -1 } } ;(@inner_elem_parse [$t :ty ] $elem :expr ) =>{{$elem .parse ::<$t >() .unwrap () } } ;($tt :tt ) =>{{use std ::io ::BufRead ;let get_stdin =std ::io ::stdin () ;let mut locked_stdin =get_stdin .lock () ;get !(@inner [&mut locked_stdin ] $tt ) } } ;}
macro_rules !debug {($($a :expr ) ,*) =>{eprintln !(concat !($(stringify !($a ) ," = {:?}, " ) ,*) ,$($a ) ,*) ;} }
macro_rules !echo {($($a :expr ) ,*) =>{let mut s =Vec ::new () ;$(s .push (format !("{}" ,$a ) ) ;) *println !("{}" ,s .join (" " ) ) ;} }
const BIG_STACK_SIZE: bool = true;
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}
#[derive(PartialEq, Eq, Debug, Clone, Copy)]
enum DKind {
    X,
    Y,
}

fn solve() {
    let n = get!(usize);
    let s = get!([chars; 2]);

    let (mut ans, mut col, mut kind) = if s[0][0] == s[1][0] {
        (3u64, 1, DKind::X)
    } else {
        (6u64, 2, DKind::Y)
    };
    while col < n {
        let v = if s[0][col] == s[1][col] {
            match kind {
                DKind::X => {
                    kind = DKind::X;
                    col += 1;
                    2
                }
                DKind::Y => {
                    kind = DKind::X;
                    col += 1;
                    1
                }
            }
        } else {
            match kind {
                DKind::X => {
                    kind = DKind::Y;
                    col += 2;
                    2
                }
                DKind::Y => {
                    kind = DKind::Y;
                    col += 2;
                    3
                }
            }
        };
        ans *= v;
        ans %= 1_000_000_007;
    }
    echo!(ans);
}