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;
#define repr(i, a, b) for (int i = a; i < b; i++)
#define rep(i, n) for (int i = 0; i < n; i++)
typedef long long ll;

int main(){
    string S;
    cin >> S;
    ll total=0,count=0;
    
    for(ll i=0;i<S.length();i++){
        if(S[i]=='>'){
            count++;
        }else{
            total+=(count+1)*count/2;
            count=0;
        }
    }
    
    
    
    total+=(count+1)*count/2;
    count=0;
    
    
    for(ll i=0;i<S.length();i++){
        if(S[i]=='<'){
            count++;
        }else{
            total+=count*(count-1)/2;
            count=0;
        }
    }
    
    total+=(count+1)*count/2;
    count=0;
    
    ll a=0,b=0,c=0;
    
    for(ll i=0;i<S.length();i++){
        if(S[i]=='<'){
            if(i!=0){
                if(S[i-1]==S[i]){
                    a++;
                }else{
                    if(a-b>0) total+=a-b;
                    a=0;
                    b=0;
                    a++;
                }
            }else{
                a++;
            }
            c=1;
        }else{
            if(c) b++;
        }
    }
    
    if(a-b>0&&S[S.length()]=='>') total+=a-b;
    
    
    
    cout << total << endl;
    

    return 0;
}