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++14 (GCC 5.4.1) (judge verdict: Accepted)


#include <algorithm>
#include <cmath>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <tuple>
#include <vector>
using namespace std;
typedef long long ll;
ll const INF = 1LL << 60;

int main() {
  string S;
  cin >> S;
  int prev = 0;
  vector<ll> ans_list(S.length() + 1, 0);
  for (int i = 0; i < S.length(); i++) {
    if (S[i] == '<') {
      ans_list[i] = 0;
      ll l_cnt = 1;
      while (S[i + l_cnt] == '<') {
        ans_list[i + l_cnt] = max(l_cnt, ans_list[i + l_cnt]);
        l_cnt++;
      }
      ans_list[i + l_cnt] = max(l_cnt, ans_list[i + l_cnt]);
      i += l_cnt - 1;
    } else {
      ll g_cnt = 1;
      while (S[i + g_cnt] == '>') g_cnt++;
      ll cnt = 0;
      for (int j = i + g_cnt; j > i; j--) {
        ans_list[j] = max(cnt, ans_list[j]);
        cnt++;
      }
      ans_list[i] = max(ans_list[i], cnt);
      i += g_cnt - 1;
    }
  }
  ll ans = 0;
  for (auto e : ans_list) {
    ans += e;
  }
  cout << ans << endl;
  return 0;
}