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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ClassLibrary1
{
    public class ListNode
    {
        public int val;
        public ListNode next;
        public ListNode(int x) { val = x; }
    }


    public class Class1
    {

        static void Main(string[] args)
        {
            char[] s = Console.ReadLine().ToCharArray();
            int[] a = new int[s.Length+1];

            int current = 0;
            int length = 0;
            int min = 0;

            a[0] = 0;
            for(int i=0; i< s.Length; i++)
            {
                if (s[i] == '<')
                {
                    current++;
                } else
                {
                    current--;
                }
                a[i + 1] = current;
                min = Math.Min(min, current);
            }

            if (min < 0)
            {
                for(int i=0;i<a.Length;i++)
                {
                    a[i] += (-1) * min;
                }
            }

            while(true)
            {
                bool flag = false;
                if (a[s.Length] > a[s.Length - 1])
                {
                    a[s.Length] = a[s.Length - 1] + 1;
                }
                else
                {
                    a[s.Length] = 0;
                }
                if (a[0] > a[1])
                {
                    a[0] = a[1] + 1;
                }
                else
                {
                    a[0] = 0;
                }
                for (int i = 0; i < s.Length - 1; i++)
                {
                    if ((a[i] > a[i + 1]) && (a[i + 1] < a[i + 2]))
                    {
                        if (a[i + 1] != 0)
                        {
                            a[i + 1] = 0;
                            flag = true;
                        }
                    }
                    if (a[i] > a[i + 1] && (a[i + 1] > a[i + 2]))
                    {
                        if ((a[i + 1] - a[i + 2] > 1))
                        {
                            a[i + 1] = a[i + 2] + 1;
                            flag = true;
                        }
                    }
                    if (a[i + 1] > a[i] && (a[i + 2] > a[i + 1]))
                    {
                        if ((a[i + 1] - a[i] > 1))
                        {
                            a[i + 1] = a[i] + 1;
                            flag = true;
                        }
                    }
                    if ((a[i] < a[i + 1]) && (a[i + 1] > a[i + 2]))
                    {
                        var m = Math.Max(a[i], a[i + 2]);
                        if( a[i+1] - m > 1)
                        {
                            a[i + 1] = m + 1;
                            flag = true;
                        }
                    }
                }
                if (!flag) break;
            }


            long sum = 0;

            for (int i = 0; i < a.Length ; i++)
            {
                sum += a[i];
            }

                Console.WriteLine(sum);

        }

        static int rec(int[] n, int i, int j, int x)
        {
            if (i + 1 == j)
            {
                return Math.Min(n[j], x);
            }
            return rec(n, i + 1, j, n[i]) + rec(n, i, j - 1, n[j]);
        }


    }
}