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>
#define ll long long
using namespace std;
int main()
{
    string s;
    ll ans = 0;
    cin >> s;
    for(int i = 0; i < (int)s.size(); ++i){
        int r = i, a = 0, b = 0;
        while(r < (int)s.size() && s[r] == '<')
            r++, a++;
        while(r < (int)s.size() && s[r] == '>')
            r++, b++;
        ans += 1LL * a * (a + 1) / 2 + 1LL * b * (b + 1) / 2 - min(a, b);
        i = r - 1;
    }
    cout << ans;
    return 0;
}
