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>
using namespace std;

int main(){
    string str;
    int64_t s = 0;
    int64_t cur = 0, l = 0;
    char prev = '>';

    cin >> str;
    str.push_back('X');
    for(int i=0;i<str.size();++i){
        if(str[i] == prev) ++cur;
        else{
            if(prev == '<'){
                if(str[i] == 'X') ++cur;
                s += cur*(cur-1) / 2;
                l = cur;
            }
            else{
                s += cur*(cur+1) / 2;
                if(cur < l) s += l-cur;
            }
            prev = str[i];
            cur = 1;
        }
    }
    cout << s << endl;

    return 0;
}