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;
typedef long long ll;

int main() {
    string s; cin >> s;
    int N = s.size() + 1;
    vector<ll> A(N);
    for(int i=0;i<N-1;++i) {
        if(s[i]=='<') 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);
    }
    ll ans = 0;
    for(int i=0;i<N;++i) ans += A[i];
    cout << ans << endl;
}