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;
typedef long long ll;

int main(){
    string s;   cin >> s;
    ll lc=0, rc=0, sum=0;
    bool f=false;
    ll n=s.size();
    vector<ll> v(n+1);
    for(int i=0; i<n; i++)
        if(s[i]=='<')
            v.at(i+1) = v.at(i)+1;
    for(int i=n-1; 0<=i; i--){
        if(s[i]=='>' && v.at(i)<=v.at(i+1))
            v.at(i) = v.at(i+1)+1; 
    }
    for(auto x: v)
        sum += x;
    cout << sum << endl;
    

}
