#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

fn solve(n: usize, c3: usize, c2: usize, c1: usize, dp: &mut Vec<Vec<Vec<Option<f64>>>>) -> f64 {
    if dp[c3][c2][c1].is_some() {
        return dp[c3][c2][c1].unwrap();
    }
    if c3 == 0 && c2 == 0 && c1 == 0 {
        dp[c3][c2][c1] = Some(0.0);
        return 0.0;
    }

    let mut res = 0.0;
    res += n as f64;
    if c3 > 0 {
        res += c3 as f64 * solve(n, c3 - 1, c2 + 1, c1, dp);
    }
    if c2 > 0 {
        res += c2 as f64 * solve(n, c3, c2 - 1, c1 + 1, dp);
    }
    if c1 > 0 {
        res += c1 as f64 * solve(n, c3, c2, c1 - 1, dp);
    }
    res /= (c1 + c2 + c3) as f64;

    dp[c3][c2][c1] = Some(res);
    // println!("{}, {}, {}, {}", c3, c2, c1, res);
    return res;
}

fn main() {
    input! {
        n: usize,
        a: [usize; n],
    }

    let c3 = a.iter().filter(|&v| *v == 3).count();
    let c2 = a.iter().filter(|&v| *v == 2).count();
    let c1 = a.iter().filter(|&v| *v == 1).count();

    let mut dp = vec![vec![vec![0.0; n + 10]; n + 10]; n + 10];

    for c3 in 0..n + 1 {
        for c2 in 0..n + 1 {
            for c1 in 0..n + 1 {
                if c3 == 0 && c2 == 0 && c1 == 0 {
                    continue;
                }

                let mut res = 0.0;
                res += n as f64;
                if c3 > 0 {
                    res += c3 as f64 * dp[c3 - 1][c2 + 1][c1];
                }
                if c2 > 0 {
                    res += c2 as f64 * dp[c3][c2 - 1][c1 + 1];
                }
                if c1 > 0 {
                    res += c1 as f64 * dp[c3][c2][c1 - 1];
                }
                res /= (c1 + c2 + c3) as f64;
                dp[c3][c2][c1] = res;
            }
        }
    }
    println!("{}", dp[c3][c2][c1]);
}


Measured memory_bytes: 252156