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<algorithm>
using namespace std;
typedef long long ll;
ll a[500010];
ll b[500010];
int main(void)
{
    ll i,n,sum=0;
    string s;
    cin >> s;
    s = '.' + s;
    for(i=1; i<s.size(); i++) {
        if(s[i]=='<')
            a[i]=a[i-1]+1;
    }
    for(i=s.size()-1; i>=1; i--) {
        if(s[i]=='>')
            b[i-1]=b[i]+1;
    }
    for(i=0;i<s.size();i++)
        sum+=max(a[i],b[i]);
    cout << sum;
    return 0;
}
