#![allow(unused_imports)]
use input::*;
use std::{
    collections::*,
    io::{self, BufWriter, Write},
};
fn run<I: Input, O: Write>(mut ss: I, mut out: O) {
    let t: u32 = 1;
    for _ in 0..t {
        case(&mut ss, &mut out);
    }
}
fn case<I: Input, O: Write>(mut ss: I, mut out: O) {
    let n: usize = ss.parse();
    let mut s: Vec<u8> = ss.parse();
    s.push(b'#');
    let mut dp = vec![L(0.0, 0.0); n + 2];
    dp[n] = L(1.0, 0.0);
    let mut dpxx = vec![0.0; n + 2];
    for i in (0..n - 1).rev() {
        if s[i] == b'.' {
            let L(a, b) = L(0.0, 3.0 / 2.0) + (dp[i + 1] + dp[i + 2]) / 2.0;
            dpxx[i] = b / (1.0 - a);
            dp[i] = L(0.0, 1.0) + (dp[i + 1] + dp[i + 2] + L(0.0, dpxx[i])) / 3.0;
        } else {
            dp[i] = L(1.0, 0.0);
        }
    }
    let ans = dpxx[0];
    wln!(out, "{}", ans);
}
#[derive(Debug, Clone, Copy)]
struct L(f64, f64);
impl std::ops::Add for L {
    type Output = Self;
    fn add(self, rhs: Self) -> Self::Output {
        L(self.0 + rhs.0, self.1 + rhs.1)
    }
}
impl std::ops::Mul<f64> for L {
    type Output = Self;
    fn mul(self, rhs: f64) -> Self::Output {
        L(self.0 * rhs, self.1 * rhs)
    }
}
impl std::ops::Div<f64> for L {
    type Output = Self;
    fn div(self, rhs: f64) -> Self::Output {
        L(self.0 / rhs, self.1 / rhs)
    }
}
fn main() {
    let stdin = io::stdin();
    let ss = SplitWs::new(stdin.lock());
    let stdout = io::stdout();
    let out = BufWriter::new(stdout.lock());
    run(ss, out);
}
pub mod input {
    use std::{
        io::{self, prelude::*},
        marker::PhantomData,
    };
    #[macro_export]
    macro_rules ! input { ($ src : expr , $ ($ var : ident $ (($ count : expr $ (, $ map : expr) ?)) ? $ (: $ ty : ty) ?) ,* $ (,) ?) => { $ (input ! (@ $ src , $ var $ (($ count $ (, $ map) ?)) ? $ (: $ ty) ?) ;) * } ; (@ $ src : expr , $ var : ident $ (: $ ty : ty) ?) => { let $ var $ (: $ ty) ? = $ src . parse () ; } ; (@ $ src : expr , $ var : ident ($ count : expr) : $ ($ ty : ty) ?) => { let $ var $ (: $ ty) ? = $ src . seq () . take ($ count) . collect () ; } ; (@ $ src : expr , $ var : ident ($ count : expr , $ map : expr) : $ ($ ty : ty) ?) => { let $ var $ (: $ ty) ? = $ src . seq () . take ($ count) . map ($ map) . collect () ; } ; }
    pub trait Input {
        fn bytes(&mut self) -> &[u8];
        fn bytes_vec(&mut self) -> Vec<u8> {
            self.bytes().to_vec()
        }
        fn str(&mut self) -> &str {
            std::str::from_utf8(self.bytes()).unwrap()
        }
        fn parse<T: Parse>(&mut self) -> T {
            self.parse_with(DefaultParser)
        }
        fn parse_with<T>(&mut self, mut parser: impl Parser<T>) -> T {
            parser.parse(self)
        }
        fn seq<T: Parse>(&mut self) -> Seq<T, Self, DefaultParser> {
            self.seq_with(DefaultParser)
        }
        fn seq_with<T, P: Parser<T>>(&mut self, parser: P) -> Seq<T, Self, P> {
            Seq {
                input: self,
                parser,
                marker: PhantomData,
            }
        }
        fn collect<T: Parse, C: std::iter::FromIterator<T>>(&mut self, n: usize) -> C {
            self.seq().take(n).collect()
        }
    }
    impl<T: Input> Input for &mut T {
        fn bytes(&mut self) -> &[u8] {
            (**self).bytes()
        }
    }
    pub trait Parser<T> {
        fn parse<I: Input + ?Sized>(&mut self, s: &mut I) -> T;
    }
    impl<T, P: Parser<T>> Parser<T> for &mut P {
        fn parse<I: Input + ?Sized>(&mut self, s: &mut I) -> T {
            (**self).parse(s)
        }
    }
    pub trait Parse {
        fn parse<I: Input + ?Sized>(s: &mut I) -> Self;
    }
    pub struct DefaultParser;
    impl<T: Parse> Parser<T> for DefaultParser {
        fn parse<I: Input + ?Sized>(&mut self, s: &mut I) -> T {
            T::parse(s)
        }
    }
    pub struct Seq<'a, T, I: ?Sized, P> {
        input: &'a mut I,
        parser: P,
        marker: PhantomData<*const T>,
    }
    impl<'a, T, I: Input + ?Sized, P: Parser<T>> Iterator for Seq<'a, T, I, P> {
        type Item = T;
        #[inline]
        fn next(&mut self) -> Option<Self::Item> {
            Some(self.input.parse_with(&mut self.parser))
        }
        fn size_hint(&self) -> (usize, Option<usize>) {
            (!0, None)
        }
    }
    impl Parse for char {
        #[inline]
        fn parse<I: Input + ?Sized>(s: &mut I) -> Self {
            let s = s.bytes();
            debug_assert_eq!(s.len(), 1);
            *s.first().expect("zero length") as char
        }
    }
    macro_rules ! tuple { ($ ($ T : ident) ,*) => { impl <$ ($ T : Parse) ,*> Parse for ($ ($ T ,) *) { # [inline] # [allow (unused_variables)] # [allow (clippy :: unused_unit)] fn parse < I : Input + ? Sized > (s : & mut I) -> Self { ($ ($ T :: parse (s) ,) *) } } } ; }
    tuple!();
    tuple!(A);
    tuple!(A, B);
    tuple!(A, B, C);
    tuple!(A, B, C, D);
    tuple!(A, B, C, D, E);
    tuple!(A, B, C, D, E, F);
    tuple!(A, B, C, D, E, F, G);
    #[cfg(feature = "newer")]
    impl<T: Parse, const N: usize> Parse for [T; N] {
        fn parse<I: Input + ?Sized>(s: &mut I) -> Self {
            use std::{
                mem::{self, MaybeUninit},
                ptr,
            };
            struct Guard<T, const N: usize> {
                arr: [MaybeUninit<T>; N],
                i: usize,
            }
            impl<T, const N: usize> Drop for Guard<T, N> {
                fn drop(&mut self) {
                    unsafe {
                        ptr::drop_in_place(&mut self.arr[..self.i] as *mut _ as *mut [T]);
                    }
                }
            }
            let mut g = Guard::<T, N> {
                arr: unsafe { MaybeUninit::uninit().assume_init() },
                i: 0,
            };
            while g.i < N {
                g.arr[g.i] = MaybeUninit::new(s.parse());
                g.i += 1;
            }
            unsafe { mem::transmute_copy(&g.arr) }
        }
    }
    macro_rules! uint {
        ($ ty : ty) => {
            impl Parse for $ty {
                #[inline]
                fn parse<I: Input + ?Sized>(s: &mut I) -> Self {
                    let s = s.bytes();
                    s.iter().fold(0, |x, d| 10 * x + (0xf & d) as $ty)
                }
            }
        };
    }
    macro_rules! int {
        ($ ty : ty) => {
            impl Parse for $ty {
                #[inline]
                fn parse<I: Input + ?Sized>(s: &mut I) -> Self {
                    let f = |s: &[u8]| {
                        s.iter()
                            .fold(0 as $ty, |x, d| (10 * x).wrapping_add((0xf & d) as $ty))
                    };
                    let s = s.bytes();
                    if let Some((b'-', s)) = s.split_first() {
                        f(s).wrapping_neg()
                    } else {
                        f(s)
                    }
                }
            }
        };
    }
    macro_rules! float {
        ($ ty : ty) => {
            impl Parse for $ty {
                fn parse<I: Input + ?Sized>(s: &mut I) -> Self {
                    const POW: [$ty; 18] = [
                        1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13,
                        1e14, 1e15, 1e16, 1e17,
                    ];
                    let s = s.bytes();
                    let (minus, s) = if let Some((b'-', s)) = s.split_first() {
                        (true, s)
                    } else {
                        (false, s)
                    };
                    let (int, fract) = if let Some(p) = s.iter().position(|c| *c == b'.') {
                        (&s[..p], &s[p + 1..])
                    } else {
                        (s, &[][..])
                    };
                    let x = int
                        .iter()
                        .chain(fract)
                        .fold(0u64, |x, d| 10 * x + (0xf & *d) as u64);
                    let x = x as $ty;
                    let x = if minus { -x } else { x };
                    let exp = fract.len();
                    if exp == 0 {
                        x
                    } else if let Some(pow) = POW.get(exp) {
                        x / pow
                    } else {
                        x / (10.0 as $ty).powi(exp as i32)
                    }
                }
            }
        };
    }
    macro_rules! from_bytes {
        ($ ty : ty) => {
            impl Parse for $ty {
                #[inline]
                fn parse<I: Input + ?Sized>(s: &mut I) -> Self {
                    s.bytes().into()
                }
            }
        };
    }
    macro_rules! from_str {
        ($ ty : ty) => {
            impl Parse for $ty {
                #[inline]
                fn parse<I: Input + ?Sized>(s: &mut I) -> Self {
                    s.str().into()
                }
            }
        };
    }
    macro_rules ! impls { ($ m : ident , $ ($ ty : ty) ,*) => { $ ($ m ! ($ ty) ;) * } ; }
    impls!(uint, usize, u8, u16, u32, u64, u128);
    impls!(int, isize, i8, i16, i32, i64, i128);
    impls!(float, f32, f64);
    impls!(from_bytes, Vec<u8>, Box<[u8]>);
    impls!(from_str, String);
    #[derive(Clone)]
    pub struct SplitWs<T> {
        src: T,
        buf: Vec<u8>,
        pos: usize,
        len: usize,
    }
    const BUF_SIZE: usize = 1 << 26;
    impl<T: Read> SplitWs<T> {
        pub fn new(src: T) -> Self {
            Self {
                src,
                buf: vec![0; BUF_SIZE],
                pos: 0,
                len: 0,
            }
        }
        #[inline(always)]
        fn peek(&self) -> &[u8] {
            unsafe { self.buf.get_unchecked(self.pos..self.len) }
        }
        #[inline(always)]
        fn consume(&mut self, n: usize) -> &[u8] {
            let pos = self.pos;
            self.pos += n;
            unsafe { self.buf.get_unchecked(pos..self.pos) }
        }
        fn read(&mut self) -> usize {
            self.buf.copy_within(self.pos..self.len, 0);
            self.len -= self.pos;
            self.pos = 0;
            if self.len == self.buf.len() {
                self.buf.resize(2 * self.buf.len(), 0);
            }
            loop {
                match self.src.read(&mut self.buf[self.len..]) {
                    Ok(n) => {
                        self.len += n;
                        return n;
                    }
                    Err(e) if e.kind() == io::ErrorKind::WouldBlock => {}
                    Err(e) => panic!("io error: {:?}", e),
                }
            }
        }
    }
    impl<T: Read> Input for SplitWs<T> {
        #[inline]
        fn bytes(&mut self) -> &[u8] {
            loop {
                if let Some(del) = self.peek().iter().position(|c| c.is_ascii_whitespace()) {
                    if del > 0 {
                        let s = self.consume(del + 1);
                        return s.split_last().unwrap().1;
                    } else {
                        self.consume(1);
                    }
                } else if self.read() == 0 {
                    return self.consume(self.len - self.pos);
                }
            }
        }
    }
}
pub mod macros {
    extern "C" {
        pub fn isatty(fd: i32) -> i32;
    }
    #[macro_export]
    macro_rules ! w { ($ dst : expr , $ ($ arg : tt) *) => { if cfg ! (debug_assertions) && unsafe { crate :: macros :: isatty (1) } != 0 { write ! ($ dst , "\x1B[1;33m") . unwrap () ; write ! ($ dst , $ ($ arg) *) . unwrap () ; write ! ($ dst , "\x1B[0m") . unwrap () ; } else { write ! ($ dst , $ ($ arg) *) . unwrap () ; } } }
    #[macro_export]
    macro_rules ! wln { ($ dst : expr $ (, $ ($ arg : tt) *) ?) => { { if cfg ! (debug_assertions) && unsafe { crate :: macros :: isatty (1) } != 0 { write ! ($ dst , "\x1B[1;33m") . unwrap () ; writeln ! ($ dst $ (, $ ($ arg) *) ?) . unwrap () ; write ! ($ dst , "\x1B[0m") . unwrap () ; } else { writeln ! ($ dst $ (, $ ($ arg) *) ?) . unwrap () ; } # [cfg (debug_assertions)] $ dst . flush () . unwrap () ; } } }
    #[macro_export]
    macro_rules! w_iter {
        ($ dst : expr , $ fmt : expr , $ iter : expr , $ delim : expr) => {{
            let mut first = true;
            for elem in $iter {
                if first {
                    w!($dst, $fmt, elem);
                    first = false;
                } else {
                    w!($dst, concat!($delim, $fmt), elem);
                }
            }
        }};
        ($ dst : expr , $ fmt : expr , $ iter : expr) => {
            w_iter!($dst, $fmt, $iter, " ")
        };
    }
    #[macro_export]
    macro_rules ! w_iter_ln { ($ dst : expr , $ ($ t : tt) *) => { { w_iter ! ($ dst , $ ($ t) *) ; wln ! ($ dst) ; } } }
    #[macro_export]
    macro_rules ! e { ($ ($ t : tt) *) => { # [cfg (debug_assertions)] eprint ! ($ ($ t) *) } }
    #[macro_export]
    macro_rules ! eln { ($ ($ t : tt) *) => { # [cfg (debug_assertions)] eprintln ! ($ ($ t) *) } }
    #[macro_export]
    #[doc(hidden)]
    macro_rules ! __tstr { ($ h : expr $ (, $ t : expr) +) => { concat ! (__tstr ! ($ ($ t) ,+) , ", " , __tstr ! (@)) } ; ($ h : expr) => { concat ! (__tstr ! () , " " , __tstr ! (@)) } ; () => { "\x1B[94m[{}:{}]\x1B[0m" } ; (@) => { "\x1B[1;92m{}\x1B[0m = {:?}" } }
    #[macro_export]
    macro_rules ! d { ($ ($ a : expr) ,*) => { if std :: env :: var ("ND") . map (| v | & v == "0") . unwrap_or (true) { eln ! (__tstr ! ($ ($ a) ,*) , file ! () , line ! () , $ (stringify ! ($ a) , $ a) ,*) ; } } ; }
}