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 <bits/stdc++.h>
using namespace std;

int main() {
    string s; cin >>s;
    long long ret = 0;
    vector<long long> v(s.size()+1);
    for (int i = 0; i <= s.size(); i++) {v[i]=0;}
    for (int i = 0; i <= s.size(); i++) {if(s[i]=='<'){v[i+1]=max(v[i+1],v[i]+1);}}
    for (int i = s.size(); i >= 0; i--) {if(s[i]=='>'){v[i]=max(v[i],v[i+1]+1);}}
    for (int i = 0; i <= s.size(); i++) ret += v[i];
    cout << ret << endl;
    return 0;
}