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 Ruby (2.3.3) (judge verdict: Accepted)

s=gets.chomp
n=s.size
u=true
i=0
cl,cg=0,0
c=0
while i<n
  if u&&s[i]=="<"
    cl+=1
  elsif u&&s[i]==">"
    cg+=1
    u=false
  elsif !u&&s[i]==">"
    cg+=1
  else
    if cl<cg
      c+=cg*(cg+1)/2+cl*(cl-1)/2
    else
      c+=cg*(cg-1)/2+cl*(cl+1)/2
    end
    u=true
    cl=1
    cg=0
  end
  i+=1
end
if cl<cg
  c+=cg*(cg+1)/2+cl*(cl-1)/2
else
  c+=cg*(cg-1)/2+cl*(cl+1)/2
end
puts c