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.Collections.Generic;
using System.Linq;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var S = Read();
            var N = S.Length + 1;
            var ans = new long[N];
            ans[N - 1] = S[S.Length - 1] == '>' ? 0 : 1;
            for (int i = S.Length - 1; i >= 0; i--) ans[i] = S[i] == '<' ? 0 : ans[i + 1] + 1;
            for (int i = 1; i < S.Length; i++)
            {
                if (S[i] == '<' && S[i - 1] == '<')
                {
                    ans[i] = Math.Max(ans[i - 1] + 1, ans[i]);
                    ans[i + 1] = Math.Max(ans[i] + 1, ans[i + 1]);
                }
            }

            Console.WriteLine(ans.Sum());
            Console.ReadKey();
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}