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>
long N=5e5,m,n,s,d=1,c;
int main(){
  c=getchar();
  while(d){
    for(m=0;c=='<';m++,c=getchar());
    for(n=0;c=='>';n++,c=getchar());
    s+=(d=(m>n?m:n)+m*(m-1)/2+n*(n-1)/2);
  }
  printf("%ld\n",s);
}
