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 <iostream>
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
vector<ll> v;
string s;
ll n,cnt,a,b,ans;
char L;
int main(void){
    cin>>s;
    n=s.size();
    L=s[0];
    if(L=='>')v.push_back(1);
    cnt=1;
    for(int i=1;i<n;i++){
        if(L!=s[i]){
            if(L=='<')v.push_back(cnt);
            else v.push_back(-cnt);
            cnt=1;
            L=s[i];
        }
        else cnt++;
    }
    if(L=='<')v.push_back(cnt);
    else v.push_back(-cnt);
    //for(auto x:v)cout<<x<<endl;
    if(v[v.size()-1]>0)v.push_back(-1);
    for(int i=0;i<v.size();i+=2){
        v[i+1]=abs(v[i+1]);
        a=max(v[i],v[i+1]);
        b=min(v[i],v[i+1]);
        ans+=a*(a+1)/2;
        ans+=b*(b-1)/2;
    }
    cout<<ans<<endl;
}