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;
    int N=s.size();
    vector<int> a(N+1,0);
    for(int i=0;i<N;i++){
        if(s[i]=='<'){
            a[i+1]=max(a[i+1],a[i]+1);
        }
    }
    for(int i=N;i>=0;i--){
        if(s[i-1]=='>'){
            a[i-1]=max(a[i-1],a[i]+1);
        }
    }
    long long sum=0;
    for(int i=0;i<=N;i++){
        //cout << a[i] << " ";
        sum+=a[i];
    }
    //cout << endl;
    cout << sum << endl;
}