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: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i, n) for(int i=0; i<n; i++)
using namespace std;
int main(void){
    string s;
    string tmp, cin_tmp;
    cin >> cin_tmp;
    s = '>' + cin_tmp + '<';
    int n = s.size();
    int st=0;
    vector<int>a(n+3,0);
    rep(i, n){
        if (s[i]=='>' and s[i+1]=='<'){
            tmp = s.substr(st, i+1-st);
            //cout << tmp << endl;
            for(int j=0; j<tmp.size(); j++) if(tmp[j]=='<') a[st+1+j] = a[st+j]+1;
            for(int j=tmp.size()-1; j>0; j--) if(tmp[j]=='>') a[st+j] = max(a[st+j+1]+1, a[st+j]);
            //for(int j=st; j< i+1; j++) cout << a[j];
            //cout << endl;
            st=i+1;
        }
    }
    if (s[n-2]=='<') a[n-1]=a[n-2]+1;
    //cout << a[n-1] << endl;
    //for(int i=1; i<n; i++) cout << a[i] << ' ';
    cout << accumulate(a.begin(), a.end(),0);
}