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 <vector>
#include <string>
#include <numeric>

using namespace std;

int main(){
    string S; cin >> S;
    vector<long long> res(S.size()+1, 0);
    for(int i=0;i<S.size();i++){
        if(S[i] == '<') res[i+1] = max(res[i+1], res[i]+1);
    }
    for(int i=S.size();i>0;i--){
        if(S[i-1] == '>') res[i-1] = max(res[i-1], res[i]+1);
    }
    cout << accumulate(res.begin(), res.end(), 0LL) << endl;
}