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-csc 3.5.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.IO;
using System.Text;
using static Scanner;
using static System.Math;

class Program
{
    static void Main(string[] args) {
        var writer = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
        Console.SetOut(writer);
        Solve();
        Console.Out.Flush();
    }
    static void Solve() {
        var S = Scan().AsSpan();
        var list = new List<string>();
        while (S.IndexOf("><", StringComparison.Ordinal) != -1) {
            list.Add(S.Slice(0, S.IndexOf("><") + 1).ToString());
            S = S[(S.IndexOf("><") + 1)..];
        }
        list.Add(S.ToString());
        long answer = 0;
        foreach (var str in list) {
            long lt = str.Length - str.Replace("<", "").Length;
            long gt = str.Length - str.Replace(">", "").Length;
            var max = Max(lt, gt);
            answer += max + lt * (lt - 1) / 2 + gt * (gt - 1) / 2;
        }
        Console.WriteLine(answer);
    }
}

public static class Scanner
{
    static readonly Stream stdin = Console.OpenStandardInput();
    static readonly byte[] buffer = new byte[1024];
    static int length, p;
    static bool isEof;
    private static byte StdIn() {
        if (isEof) return 0;
        if (p < length) return buffer[p++];
        p = 0;
        if ((length = stdin.Read(buffer, 0, 1024)) > 0) return buffer[p++];
        isEof = true;
        return 0;
    }
    public static char GetChar() {
        var by = StdIn();
        while ((by < '!' || '~' < by) && !isEof) by = StdIn();
        return (char) by;
    }
    public static string Scan() {
        var sb = new StringBuilder();
        for (var ch = GetChar(); '!' <= ch && ch <= '~'; ch = (char) StdIn()) {
            sb.Append(ch);
        }
        return sb.ToString();
    }
}