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

class A
{
	static void Main()
	{
		var s = Console.ReadLine();

		long t = 0, r = 0;
		foreach (var g in s.GroupBySeq(x => x).Select(g => new { g.Key, c = g.LongCount() }))
			r += g.Key == '<' ? (t = g.c) * (t + 1) / 2 : Math.Max(0, g.c - t) + g.c * (g.c - 1) / 2;
		Console.WriteLine(r);
	}
}

static class GE
{
	public static IEnumerable<IGrouping<TK, TS>> GroupBySeq<TS, TK>(this IEnumerable<TS> source, Func<TS, TK> toKey)
	{
		var c = EqualityComparer<TK>.Default;
		var k = default(TK);
		var l = new List<TS>();

		foreach (var o in source)
		{
			var kt = toKey(o);
			if (!c.Equals(kt, k))
			{
				if (l.Count > 0) yield return new G<TK, TS>(k, l.ToArray());
				k = kt;
				l.Clear();
			}
			l.Add(o);
		}
		if (l.Count > 0) yield return new G<TK, TS>(k, l.ToArray());
	}

	class G<TK, TE> : IGrouping<TK, TE>
	{
		public TK Key { get; }
		IEnumerable<TE> Values;
		public G(TK key, TE[] values) { Key = key; Values = values; }

		public IEnumerator<TE> GetEnumerator() => Values.GetEnumerator();
		IEnumerator IEnumerable.GetEnumerator() => GetEnumerator();
	}
}