Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

<>>

Sample Output 1

3

a=(0,2,1,0) is a good sequence whose sum is 3.
There is no good sequence whose sum is less than 3.

Sample Input 2

<>>><<><<<<<>>><

Sample Output 2

28

Solution in Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program AGC40
  character(500000)::S
  integer(8),allocatable::A(:)
  read(*,*)S
  N=len_trim(S)+1
  allocate(A(N))
  A=500000
  if(S(1:1)=='<') A(1)=0
  if(S(N-1:N-1)=='>') A(N)=0
  do i=1,N-1
     if(S(i:i)=='>' .and. S(i+1:i+1)=='<') A(i+1)=0
  end do
  do i=1,N-1
     if(S(i:i)=='<') A(i+1)=A(i)+1
  end do
  do i=N,2,-1
     if(S(i-1:i-1)=='>' .and. (A(i-1)==500000 .or. A(i-1)<=A(i))) A(i-1)=A(i)+1        
  end do
  write(*,*)sum(A)
end program AGC40