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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int main() {
    string s;
    cin >> s;

    vector<int> a(s.size()+1, 0);
    for (int i = 0; i < s.size(); i++) {
        if (s[i] == '<') a[i+1] = a[i] + 1;
    }
    for (int i = s.size()-1; i >= 0; i--) {
        if (s[i] == '>') a[i] = max (a[i], a[i+1]+1);
    }
    long long ans = 0;
    for (int i = 0; i <= s.size(); i++) ans += a[i];
    cout << ans << endl;
}