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.

Examples

Input

<>>


Output

3


Input

<>>><<><<<<<>>><


Output

28
#include<iostream>
#include<numeric>
#include<vector>
using namespace std;
using ll = long long;

int main(){
    string s;
    cin>>s;
    int n=(int)s.length()+1;
    vector<ll> v(n+1);
    for(int i=0;i<n;i++){
        if(s[i]=='<') v[i+1]=max(v[i]+1,v[i+1]);
    }
    for(int i=n-1;i>=0;i--){
        if(s[i]=='>') v[i]=max(v[i+1]+1,v[i]);
    }
    cout<<accumulate(v.begin(),v.end(),0LL)<<endl;
}