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>
#define rep(i, n) for (int i=0;i<(n);i++)
using namespace std;
typedef long long ll;
 
int main(void){
    string s;
    cin>>s;
    vector<ll> ans(s.size()+1);
    ll nowl=0;
    rep(i, s.size()){
        if(s[i] == '<'){
            ans[i]=nowl;
            nowl++;
            ans[i+1]=nowl;
        }
        else nowl=0;
    }
    reverse(s.begin(), s.end());
    ll nowr=0;
    rep(i, s.size()){
        if(s[i] == '>'){
            ans[s.size()-i]=max(nowr, ans[s.size()-i]);
            nowr++;
            ans[s.size()-i-1]=max(nowr, ans[s.size()-i-1]);
        }
        else nowr=0;
    }
    ll sum = accumulate(ans.begin(), ans.end(), 0LL);
    cout<<sum<<endl;
    return 0;
}