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>
#define N 500005
using namespace std;
char s[N];
int f[N];
int main() {
    scanf("%s", s + 1);
    int n = strlen(s + 1) + 1;
    for(int i = n - 1; i; -- i)
        if(s[i] == '<') f[i] = 0;
        else f[i] = f[i + 1] + 1;
    for(int i = 1; i < n; ++ i)
        if(s[i] == '<') f[i + 1] = max(f[i + 1], f[i] + 1);
    long long ans = 0;
    for(int i = 1; i <= n; ++ i) ans += f[i];
    cout << ans << endl;
}