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;

const int N = 500010;

char s[N];
int l[N], r[N];

typedef long long LL;

int main() {
  scanf("%s", s + 1);
  int n = strlen(s + 1);
  for (int i = 1; i <= n; ++i)
    l[i] = (s[i] == '<') ? l[i - 1] + 1 : 0;
  for (int i = n; i >= 1; --i)
    r[i] = (s[i] == '>') ? r[i + 1] + 1 : 0;
  LL ans = 0;
  for (int i = 0; i <= n; ++i)
    ans += max(l[i], r[i + 1]);
  printf("%lld\n", ans);
  return 0;
}