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<int> A(s.size() + 1);
    for (int i = 0; i < s.size(); ++i)
        if (s.at(i) == '<')
            A[i + 1] = max(A[i + 1], A[i] + 1);

    for (int i = s.size() - 1; i >= 0; --i)
        if (s.at(i) == '>')
            A[i] = max(A[i], A[i + 1] + 1);

    long long ans = 0;
    for (int i = 0; i <= s.size(); ++i)
        ans += A[i];
    cout << ans << endl;
    return 0;
}

