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 n = s.size();
    vector<ll> l(n+1),r(n+1);
    for(ll i=1; i<=n; i++) {
        if(s[i-1] == '<') l[i] = l[i-1]+1;
    }
    for(ll i=n-1; i>=0; i--) {
        if(s[i] == '>') r[i] = r[i+1]+1;
    }
    vector<ll> a(n+1);
    for(ll i=0; i<=n; i++) {
        a[i] = max(l[i],r[i]);
    }
    cout<<accumulate(a.begin(),a.end(),0LL);
}