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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using static System.Console;
using static System.Math;

class Program
{
    static void Main()
    {
        var S = ReadLine();
        var N = S.Length + 1;
        var a = new int[N];
        for (int i = 0; i < N; i++)
        {
            a[i] = -1;
        }
        for (int i = 0; i < S.Length - 1; i++)
        {
            if (S[i] == '>' && S[i + 1] == '<') a[i + 1] = 0;
        }
        if (S[0] == '<') a[0] = 0;
        if (S[N - 2] == '>') a[N - 1] = 0;
        for (int i = 0; i < N; i++)
        {
            if (a[i] != 0) continue;
            for (int j = i + 1; j < N; j++)
            {
                if (S[j - 1] == '>') break;
                var b = a[j - 1] + 1;
               if(a[j]<b) a[j] =b;
            }
            for (int j = i - 1; j >= 0; j--)
            {
                if (S[j] == '<') break;
                var b= a[j + 1] + 1;
                if (a[j] < b) a[j] = b;
            }
        }

        WriteLine(a.Sum());

    }
}