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;
    int N = S.size() + 1;
    vector<int> A(N,0);
    for(int i = 0; i < N-1; ++i) {
        if(S[i] == '<') A[i+1] = max(A[i+1], A[i]+1);
    }
    for(int i = N-2; i >= 0; --i) {
        if(S[i] == '>') A[i] = max(A[i], A[i+1]+1);
    }
    long long res = 0LL;
    for(auto &p: A) res += p;
    cout << res << endl;
    return 0;
}