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;

    vector<long long> a(s.size()+1, 0);
    for (int i = 0; i < s.size(); i++) {
        if (s[i] == '<') a[i+1] = a[i] + 1;
    }
    for (int i = s.size()-1; i >= 0; i--) {
        if (s[i] == '>') a[i] = max (a[i], a[i+1]+1);
    }
    long long ans = accumulate (a.begin(), a.end(), 0LL);
    cout << ans << endl;
}
