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();
    vector<int> A(N + 1), B(N + 1);
    for(int i = 0; i < N; ++i) if(S[i] == '<') A[i + 1] = A[i] + 1;
    for(int i = N - 1; i >= 0; --i) if(S[i] == '>') B[i] = B[i + 1] + 1;
    int64_t ans = 0;
    for(int i = 0; i <= N; ++i) ans += max(A[i], B[i]);
    cout << ans << '\n';
    return 0;
}
