#[allow(unused_imports)]
use std::cmp::Ordering;

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};

#[allow(unused_imports)]
use std::iter::FromIterator;

#[allow(unused_macros)]
macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::min($x, min!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::max($x, max!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! get {
    ([$t: ty]) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            line.split_whitespace().map(|t|t.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    };
    ([$t: ty];$n: expr) => {
        (0..$n).map(|_|get!([$t])).collect::<Vec<_>>()
    };
    ($t: ty) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t: ty),*) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
    ($t: ty; $n: expr) => {
        (0..$n).map(|_|get!($t)).collect::<Vec<_>>()
    };
    ($($t: ty),*; $n: expr) => {
        (0..$n).map(|_|get!($($t),*)).collect::<Vec<_>>()
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

const BIG_STACK_SIZE: bool = true;

#[allow(dead_code)]
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();
    }
}

fn dfs(one: usize, two: usize, three: usize, n: usize, dp: &mut Vec<Vec<Vec<Option<f64>>>>) -> f64 {
    if let Some(val) = dp[one][two][three] {
        return val;
    }

    let s = one + two + three;

    let mut val = 0.0;
    val += if one > 0 {
        dfs(one - 1, two, three, n, dp) * one as f64 / s as f64
    } else {
        0.0
    };
    val += if two > 0 {
        dfs(one + 1, two - 1, three, n, dp) * two as f64 / s as f64
    } else {
        0.0
    };
    val += if three > 0 {
        dfs(one, two + 1, three - 1, n, dp) * three as f64 / s as f64
    } else {
        0.0
    };

    val += n as f64 / s as f64;

    dp[one][two][three] = Some(val);
    val
}

fn solve() {
    let n = get!(usize);
    let a = get!([usize]);

    let mut one = 0;
    let mut two = 0;
    let mut three = 0;
    for e in a {
        if e == 1 {
            one += 1;
        } else if e == 2 {
            two += 1;
        } else {
            three += 1;
        }
    }

    let mut dp = vec![vec![vec![None; n + 1]; n + 1]; n + 1];
    dp[0][0][0] = Some(0.0);
    let val = dfs(one, two, three, n, &mut dp);
    println!("{}", val);
}


Measured memory_bytes: 473468