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 <string>
# include <vector>


using namespace std;


int main() {
    string s;
    cin >> s;

    int n = s.size();
    vector<int> a(n+1, 0);

    for (int i=0; i<n; i++) {
        if (s[i] == '<') a[i+1] = a[i] + 1;
    }

    for (int i=n-1; 0<=i; i--) {
        if (s[i] == '>' and a[i] <= a[i+1]) a[i] = a[i+1] + 1;
    }

    long long ans = 0;
    for (int ai: a) {
        ans += ai;
    }
    cout << ans << endl;
}
