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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using System.Text;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var n = consoleReader.Int;
            var s = consoleReader.String;

            var eSum = new int[s.Length + 1];
            for (int i = 0; i < s.Length; i++)
                eSum[i + 1] = eSum[i] + (s[i] == 'E' ? 1 : 0);
            var min = int.MaxValue;

            for (int i = 0; i < s.Length; i++)
            {
                var leftE = eSum[i];
                var leftW = i - leftE;
                var rightE = eSum[s.Length] - eSum[i + 1];

                min = Math.Min(min, leftW + rightE);
            }


            return min;
        }

        #region いつもの
        private readonly ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
        #endregion
    }

#pragma warning disable
    public class ConsoleReader
    {
        private string[] line = Array.Empty<string>();
        private int linePosition;
        private TextReader textReader;
        public ConsoleReader(TextReader tr) { textReader = tr; }
        public int Int => int.Parse(String);
        public long Long => long.Parse(String);
        public double Double => double.Parse(String);
        public string String
        {
            get
            {
                if (linePosition >= line.Length)
                {
                    linePosition = 0;
                    line = textReader.ReadLine().Split();
                }
                return line[linePosition++];
            }
        }
        public class SplitLine
        {
            private string[] splited;
            public SplitLine(ConsoleReader cr) { splited = cr.textReader.ReadLine().Split(); }
            public int[] Int => String.Select(x => int.Parse(x)).ToArray();
            public long[] Long => String.Select(x => long.Parse(x)).ToArray();
            public double[] Double => String.Select(x => double.Parse(x)).ToArray();
            public string[] String => splited;
        }
        public SplitLine Split => new SplitLine(this);
        public class RepeatReader
        {
            ConsoleReader cr; int count;
            public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; }
            public IEnumerable<T> Select<T>(Func<ConsoleReader, T> func) { for (int i = 0; i < count; i++) yield return func(cr); }
            public IEnumerable<string> String { get { for (int i = 0; i < count; i++) yield return cr.String; } }
            public IEnumerable<int> Int { get { for (int i = 0; i < count; i++) yield return cr.Int; } }
            public IEnumerable<double> Double { get { for (int i = 0; i < count; i++) yield return cr.Double; } }
        }
        public RepeatReader Repeat(int count) => new RepeatReader(this, count);
    }
}