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 <iostream>
#include <iomanip>
#include <string>
#include <vector>
#include <cmath>
#include <algorithm>
#include <limits>
#include <sstream>
#include <fstream>
#include <climits>
#include <map>
#include <numeric>
#include <functional>
#include <utility>

using namespace std;

#define rep(i, n) for (int i = 0; i < (n); ++i)
typedef long long ll;
typedef unsigned long long ull;

int main(void) {
  string s;
  cin >> s;
  int n = s.size() + 1;
  vector<ull> left(n, 0), right(n, 0);
  for (int i = 1; i <= n - 1; i++) {
    if (s.at(i - 1) == '<') left.at(i) = left.at(i - 1) + 1;
  }
  for (int i = n - 2; i >= 0; i--) {
    if (s.at(i) == '>') right.at(i) = right.at(i + 1) + 1;
  }
  vector<ull> mx(n);
  ull ans = 0;
  rep(i, n) {
    mx.at(i) = max(left.at(i), right.at(i));
    ans += mx.at(i);
  }

  cout << ans << endl;

  return 0;
}