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<bits/stdc++.h>
#define watch(x) cout << (#x) << " is " << (x) << endl
typedef long long ll;
using namespace std;
int static fast = [](){
  ios::sync_with_stdio(false);
  cin.tie(0); cout.tie(0); return 0;
}();

void sub(vector<ll>& arr, char pre, char post, string s) {
    ll cur = 0;
    for(int i = 0; i < s.size(); i++) {
        if (s[i] == pre) {
            if (i == 0 || s[i-1] == post) {
                cur = 0;
            }
            arr[i] = cur++;
        } else if (s[i] == post) {
            arr[i] = max(arr[i], cur);
            cur = 0;
        }
    }
    if (s.back() == pre)
        arr[arr.size()-1] = cur;
}

int main() {
    string s;
    cin >> s;
    vector<ll> arr(s.size()+1, INT_MIN);
    sub(arr, '<', '>', s);
    reverse(arr.begin(), arr.end());
    reverse(s.begin(), s.end());
    sub(arr, '>', '<', s);
    reverse(arr.begin(), arr.end());
    
    cout << accumulate(arr.begin(), arr.end(), 0LL) << endl;
    return 0;
}