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<iostream>
using namespace std;
int f(int n){
    return n*(n+1)/2;
}
int main(){
    string s,r;
    cin>>s;
    int ans=0,c=1,m=0,bc=0;
    char b;
    for(int i=1;i<s.size();i++){
        if(s[i-1]==s[i])c++;
        else {
            if(s[i]=='>'){
                bc=c;
            }
            else m+=min(c,bc);
            ans+=f(c);
            c=1;
        }
    }
    ans+=f(c);
    if(s[s.size()-1]=='>')m+=min(c,bc);
    cout<<ans-m<<endl;
    return 0;
}