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>

const int N=5e5;
inline char* l(char* p, int s) { for(;*p==s;p++); return p; }

int main(int argc, char* argv[])
{
  int64_t sum=0;
  char s[N+1];
  char *p,*q,*r;
  scanf("%s",s);
  for (p=s;*p;p=r) {
    q=l(p,'<'), r=l(q,'>');
    int64_t m=q-p, n=r-q;
    sum += m*(m-1)/2 + n*(n-1)/2 + ((m>n)?m:n);
  }
  printf("%ld\n", sum);
  return 0;
}

