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 S;
    cin >> S;
    bool up,first=true;
    long long int ans=0,count=1,last=0;
    if(S[0]=='<'){
        up = true;
    }else{
        up = false;
    }

    for(int i=1;i<S.size();i++){
        first=false;
        if(S[i]=='<' && up){
            count++;
        }else if(S[i]=='>' && !up){
            count++;
        }else{
            if(up){
                if(count!=1){
                    ans += count*(count+1)/2;
                }else{
                    ans++;
                }
                last = count;
                up = false;
            }else{
                if(count!=1){
                    ans += count*(count-1)/2;
                }

                if(last<count){
                    ans += count-last;
                }
                last = count;
                up=true;
            }
            count=1;
        }
    }

    if(up){
                if(count!=1){
                    ans += count*(count+1)/2;
                }else{
                    ans++;
                }
                last = count;
            }else{
                if(count!=1){
                    ans += count*(count-1)/2;
                }

                if(last<count){
                    ans += count-last;
                }
            }
            
        cout << ans << endl;
}