Problem:
Score : 300 points

Problem Statement

There are N stones arranged in a row. Every stone is painted white or black.
A string S represents the color of the stones. The i-th stone from the left is white if the i-th character of S is ., and the stone is black if the character is #.

Takahashi wants to change the colors of some stones to black or white so that there will be no white stone immediately to the right of a black stone.
Find the minimum number of stones that needs to be recolored.

Constraints

1 \leq N \leq 2\times 10^5

S is a string of length N consisting of . and #.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the minimum number of stones that needs to be recolored.

Sample Input 1

3
#.#

Sample Output 1

1

It is enough to change the color of the first stone to white.

Sample Input 2

5
#.##.

Sample Output 2

2

Sample Input 3

9
.........

Sample Output 3

0

Solution in Rust (1.15.1) (judge verdict: Runtime Error)

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)*}
    };
}

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)*}
    };
}

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>>()
    };

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

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

const md : i64 = 998244353;

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

    let mut pow3 = vec![1; n+1];
    let mut pow2 = vec![1; n+1];
    for i in 0..n {
        pow3[i+1] = (pow3[i] * 3) % md;
        pow2[i+1] = (pow2[i] * 2) % md;
    }
    let al : i64 = pow3[n] - 3 * pow2[n] + 3;
    
    let mut sm : usize = 0;
    for i in 0..n {sm += a[i];}
    let mut dp = vec![vec![0i64; sm+1] ; n+1];
    dp[0][0] = 1;
    for i in 0..n {
        let ai = a[i];
        for k in (1..(n+1)).rev() {
            for s in (0..(sm+1)).rev() {
                if s >= ai {
                    //println!("<-[{}][{}]={}",k-1, s-ai, dp[(k-1) as usize][(s-ai) as usize]);
                    dp[k][s] += dp[(k-1) as usize][(s-ai) as usize];
                    dp[k][s] = dp[k][s] % md;
                    //println!("k={}, s={}, i={} => dp[k][s]={}",k,s,i,dp[k][s]);
                }
            }
        }
    }
    //println!("{}", dp[2][4]);

    let mut ng : i64 = 0;
    for s in ((sm+1) / 2)..(sm + 1) {
        for k in 1..(n-2+1) {
            let cm = dp[k][s]; 
            let r =  (cm * 3 * (pow2[(n - k) as usize] - 2))%md;
            //println!("k={}, s={}, n-k={}, cm={} => {}", k, s, n-k, cm, r);
            ng = (ng + r) % md;
        }
    }

    //println!("{}, {}", al, ng);
    println!("{}", ((al%md - ng%md)+10*md) %md);
}