Problem:
Score : 300 points

Problem Statement

There are N people standing in a row from west to east.
Each person is facing east or west.
The directions of the people is given as a string S of length N.
The i-th person from the west is facing east if S_i = E, and west if S_i = W.

You will appoint one of the N people as the leader, then command the rest of them to face in the direction of the leader.
Here, we do not care which direction the leader is facing.

The people in the row hate to change their directions, so you would like to select the leader so that the number of people who have to change their directions is minimized.
Find the minimum number of people who have to change their directions.

Constraints

2 \leq N \leq 3 \times 10^5

|S| = N

S_i is E or W.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the minimum number of people who have to change their directions.

Sample Input 1

5
WEEWW

Sample Output 1

1

Assume that we appoint the third person from the west as the leader.
Then, the first person from the west needs to face east and has to turn around.
The other people do not need to change their directions, so the number of people who have to change their directions is 1 in this case.
It is not possible to have 0 people who have to change their directions, so the answer is 1.

Sample Input 2

12
WEWEWEEEWWWE

Sample Output 2

4

Sample Input 3

8
WWWWWEEE

Sample Output 3

3

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

use io::*;
use std::cmp::min;

struct BIT {
    v: Vec<i64>,
}

impl BIT {
    fn new(n: usize) -> BIT {
        BIT { v: vec![0; n + 1] }
    }

    fn sum(&self, i: usize) -> i64 {
        if i == 0 {
            0
        } else {
            let ii = i as i64;
            self.v[i] + self.sum(i - (ii & (-ii)) as usize)
        }
    }

    fn add(&mut self, i: usize, x: i64) {
        if i < self.v.len() {
            self.v[i] += x;
            let ii = i as i64;
            self.add(i + (ii & (-ii)) as usize, x);
        }
    }
}

fn main() {
    let con = read_string();
    let mut sc = Scanner::new(&con);

    let n: usize = sc.next();
    let s: String = sc.next();
    let s: Vec<char> = s.chars().collect();

    let mut ws = BIT::new(n);
    let mut es = BIT::new(n);

    for i in 1..n + 1 {
        ws.add(i, if s[i - 1] == 'W' { 1 } else { 0 });
        es.add(i, if s[i - 1] == 'E' { 1 } else { 0 });
    }

    let mut ans = (n + 1) as i64;
    for i in 1..n + 1 {
        let l = if i == 1 { 0 } else { ws.sum(i - 1) };
        let r = if i == n { 0 } else { es.sum(n) - es.sum(i) };

        let cur = l + r;
        ans = min(ans, cur);
    }

    println!("{}", ans);
}

//-----

pub mod io {
    use std;
    use std::str::FromStr;

    pub struct Scanner<'a> {
        iter: std::str::SplitWhitespace<'a>,
    }

    impl<'a> Scanner<'a> {
        pub fn new(s: &'a str) -> Scanner<'a> {
            Scanner {
                iter: s.split_whitespace(),
            }
        }

        pub fn next<T: FromStr>(&mut self) -> T {
            let s = self.iter.next().unwrap();
            if let Ok(v) = s.parse::<T>() {
                v
            } else {
                panic!("Parse error")
            }
        }

        pub fn next_vec_len<T: FromStr>(&mut self) -> Vec<T> {
            let n: usize = self.next();
            self.next_vec(n)
        }

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

    pub fn read_string() -> String {
        use std::io::Read;

        let mut s = String::new();
        std::io::stdin().read_to_string(&mut s).unwrap();
        s
    }

    pub fn read_line() -> String {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        s.trim_right().to_owned()
    }
}