Problem:
Score : 300 points

Problem Statement

Given is a string S of length N-1.
Each character in S is < or >.

A sequence of N non-negative integers, a_1,a_2,\cdots,a_N, is said to be good when the following condition is satisfied for all i (1 \leq i \leq N-1):

If S_i= <: a_i<a_{i+1}

If S_i= >: a_i>a_{i+1}

Find the minimum possible sum of the elements of a good sequence of N non-negative integers.

Constraints

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

S is a string of length N-1 consisting of < and >.

Input

Input is given from Standard Input in the following format:

S

Output

Find the minimum possible sum of the elements of a good sequence of N non-negative integers.

Sample Input 1

<>>

Sample Output 1

3

a=(0,2,1,0) is a good sequence whose sum is 3.
There is no good sequence whose sum is less than 3.

Sample Input 2

<>>><<><<<<<>>><

Sample Output 2

28

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

using System;
using System.Linq;
using System.Collections.Generic;
using System.Collections;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var S = Console.ReadLine();
            var counter = new List<int>();
            var cur = S[0];
            var count = 1;

            for (var i = 1; i < S.Length; i++)
            {
                if (cur == S[i])
                    count++;
                else
                {
                    counter.Add(count);
                    count = 1;
                    cur = S[i];
                }
            }

            counter.Add(count);

            if (counter.Count == 1)
            {
                Console.WriteLine(SumVal(counter[0]));
                return;
            }

            if (counter.Count == 2 && S[0] == '>' && S[S.Length-1] == '<')
            {
                Console.WriteLine(SumVal(counter[0]) + SumVal(counter[1]));
                return;
            }

            var start = S[0] == '<' ? 1 : 2;
            decimal ans = 0;
            if (counter.Count % 2 == 1)
                ans = S[0] == '<' ? SumVal(counter[counter.Count - 1]) : SumVal(counter[0]);
            if (counter.Count % 2 == 0 && S[0] == '>' && S[S.Length - 1] == '<')
                ans = SumVal(counter[0]) + SumVal(counter[counter.Count - 1]);

            for (var i = start; i < counter.Count; i+=2)
            {
                if (counter[i] >= counter[i - 1])
                    counter[i - 1]--;
                else
                    counter[i]--;

                ans += SumVal(counter[i]);
                ans += SumVal(counter[i - 1]);
            }

            Console.WriteLine(ans);
        }

        static decimal SumVal(int a)
        {
            return (decimal)(a * 0.5 * (a + 1));
        }
    }
}