Problem:
Score : 600 points

Problem Statement

You are given a string S of length 2N consisting of lowercase English letters.

There are 2^{2N} ways to color each character in S red or blue. Among these ways, how many satisfy the following condition?

The string obtained by reading the characters painted red from left to right is equal to the string obtained by reading the characters painted blue from right to left.

Constraints

1 \leq N \leq 18

The length of S is 2N.

S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the number of ways to paint the string that satisfy the condition.

Sample Input 1

4
cabaacba

Sample Output 1

4

There are four ways to paint the string, as follows:

cabaacba

cabaacba

cabaacba

cabaacba

Sample Input 2

11
mippiisssisssiipsspiim

Sample Output 2

504

Sample Input 3

4
abcdefgh

Sample Output 3

0

Sample Input 4

18
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Sample Output 4

9075135300

The answer may not be representable as a 32-bit integer.

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

#![allow(unused_imports, unused_macros, dead_code)]
use std::f64::*;
use std::cmp::*;
use std::collections::*;
use std::ops::*;

macro_rules! dump{
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        eprintln!(
            concat!("{}:{}:{}: ",$(stringify!($a), " = {:?}, "),*),
            file!(), line!(), column!(), $($a),*
        );
        #[cfg(not(debug_assertions))]
        {};
    }
}

const INF: i64 = 0x3f3f3f3f3f3f3f3f;
const MOD: i64 = 1000000007;
const NOTHING: usize = std::usize::MAX;
const DX: [usize; 4] = [1, 0, std::usize::MAX, 0];
const DY: [usize; 4] = [0, 1, 0, std::usize::MAX];

fn solve<R: std::io::BufRead, W: std::io::Write>(io: &mut IO<R, W>) {
    let n: usize = io.readln();
    let cs: Vec<char> = io.readln();
    let mut cs_r: Vec<char> = cs[n..2 * n].to_vec();
    cs_r.reverse();

    let mut freq: HashMap<String, usize> = HashMap::new();
    for set in 0..1 << n {
        let mut red = String::with_capacity(n + 1);
        let mut blue = String::new();
        for i in 0..n {
            if set & (1 << i) != 0 {
                red.push(cs_r[i]);
            } else {
                blue.push(cs_r[i]);
            }
        }
        red.push(' ');
        red.push_str(&blue);
        *freq.entry(red).or_insert(0) += 1;
    }

    let mut res = 0;
    for set in 0..1 << n {
        let mut red = String::with_capacity(n + 1);
        let mut blue = String::new();
        for i in 0..n {
            if set & (1 << i) != 0 {
                red.push(cs[i]);
            } else {
                blue.push(cs[i]);
            }
        }
        red.push(' ');
        red.push_str(&blue);
        res += *freq.get(&red).unwrap_or(&0usize);
    }
    io.writeln(res);
}

fn main() {
    use std::io::*;
    std::thread::Builder::new()
        .stack_size(32 * 1024 * 1024)
        .spawn(|| {
            let stdin = stdin();
            let stdout = stdout();
            let mut io = IO::new(BufReader::new(stdin.lock()), BufWriter::new(stdout.lock()));
            solve(&mut io);
            io.flush();
        })
        .unwrap()
        .join()
        .unwrap();
}

pub struct IO<R, W> {
    reader: R,
    writer: W,
}

impl<R: ::std::io::BufRead, W: ::std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> IO<R, W> {
        IO {
            reader: r,
            writer: w,
        }
    }

    pub fn readln<T: UnsafeFromStr>(&mut self) -> T {
        let mut buf = Vec::new();
        self.reader.read_until(b'\n', &mut buf).unwrap();
        let token = unsafe { ::std::str::from_utf8_unchecked(&buf) };
        T::unsafe_from_str(token.trim_right())
    }

    pub fn readlns<T: UnsafeFromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.readln()).collect()
    }

    pub fn write<T: ::std::fmt::Display>(&mut self, x: T) {
        self.writer.write_fmt(format_args!("{}", x)).unwrap();
    }
    pub fn writeln<T: ::std::fmt::Display>(&mut self, x: T) {
        self.writer.write_fmt(format_args!("{}\n", x)).unwrap();
    }

    pub fn writes<T: ::std::fmt::Display>(&mut self, xs: &Vec<T>, sep: &str) {
        let mut it = xs.iter();
        for &x in it.next().iter() {
            self.write(x);
        }
        for x in it {
            self.writer.write(sep.as_bytes()).unwrap();
            self.write(x);
        }
    }

    pub fn writesln<T: ::std::fmt::Display>(&mut self, xs: &Vec<T>, sep: &str) {
        self.writes(xs, sep);
        self.writer.write(b"\n").unwrap();
    }

    pub fn flush(&mut self) {
        self.writer.flush().unwrap()
    }
}

pub trait UnsafeFromStr {
    fn unsafe_from_str(s: &str) -> Self;
}

impl UnsafeFromStr for char {
    fn unsafe_from_str(s: &str) -> char {
        s.chars().next().unwrap()
    }
}

impl UnsafeFromStr for Vec<char> {
    fn unsafe_from_str(s: &str) -> Vec<char> {
        s.chars().collect()
    }
}

macro_rules! unsafe_from_str_impl{
    ($($t:ty)*) => ($(
        impl UnsafeFromStr for $t {
            fn unsafe_from_str(s: &str) -> $t{
                s.parse().unwrap()
            }
        }
        impl UnsafeFromStr for Vec<$t> {
            fn unsafe_from_str(s: &str) -> Vec<$t>{
                s.split_whitespace().map(|t| t.parse().unwrap()).collect()
            }
        }
    )*)
}
unsafe_from_str_impl!{ usize u8 u16 u32 u64 isize i8 i16 i32 i64 f32 f64 }

macro_rules! unsafe_from_str_tuple_impl{
    ($($t:ident),+) => {
        impl<$($t: UnsafeFromStr),*> UnsafeFromStr for ($($t),*) {
            fn unsafe_from_str(s: &str) -> Self {
                let mut tokens = s.split_whitespace();
                ($($t::unsafe_from_str(tokens.next().unwrap())),+)
            }
        }
    }
}
unsafe_from_str_tuple_impl!(A, B);
unsafe_from_str_tuple_impl!(A, B, C);
unsafe_from_str_tuple_impl!(A, B, C, D);
unsafe_from_str_tuple_impl!(A, B, C, D, E);