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>

int main(){
    using namespace std;
    string s;
    cin >> s;
    unsigned long N{s.size()};
    vector<unsigned long> l(N + 1), r(N + 1);
    for(unsigned long i = 0; i < N; ++i)l[i + 1] = s[i] == '<' ? l[i] + 1 : 0;
    for(unsigned long i = N; i--; )r[i] = s[i] == '>' ? r[i + 1] + 1 : 0;
    unsigned long ans{0};
    for(unsigned long i = 0; i <= N; ++i)ans += max(l[i], r[i]);
    cout << ans << endl;
    return 0;
}