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: Wrong Answer)

using System;
class p
{
  static void Main()
  {
    string S = Console.ReadLine();
    
    // 先頭が<>になるよう成型
    if (S[0] == '>') {
      S = "<" + S;
    }
    // 末尾が<>になるよう成型
    if (S[S.Length - 1] == '<') {
      S = S + ">";
    }
    
    int index = S.IndexOf("<>", 0), sum = 0;
    if (0 <= index) {
      while (0 <= index) {
        // < の数
        int cntA = 0;
        for (int i = index; 0 <= i; i--) {
          if (S[i] == '<') { cntA++; }
          else { break; }
        }
        // > の数
        int cntB = 0;
        for (int i = index + 1; i < S.Length; i++) {
          if (S[i] == '>') { cntB++; }
          else { break; }
        }
        // 大きい方はmax値から順に足す
        int max = Math.Max(cntA, cntB);
        for (int i = 1; i <= max; i++) {
          sum += i;
        }
        // 小さいほうは0から順に足す
        int min = Math.Min(cntA, cntB);
        for (int i = 0; i < min; i++) {
          sum += i;
        }
        // 再検索
        index = (index + 1 < S.Length) ? S.IndexOf("<>", index + 1) : -1;
      }
      // 先頭の>の数
      int cntC = 0;
      for (int i = 0; i < S.Length; i++) {
        if (S[i] == '>') { cntC++; }
        else { break; }
      }
      // 末尾の<の数
      int cntD = 0;
      for (int i = S.Length - 1; 0 <= i; i--) {
        if (S[i] == '<') { cntD++; }
        else { break; }
      }
      sum += (cntC + cntD);
    }
    Console.WriteLine(sum);
  }
}