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
s="<"+s if s[0]==">"
s=s+">" if s[s.size-1]=="<"
n=s.size
cnt=0
l,r=0,0
n.times do |i|
  if s[i]=="<"
    l+=1
  else
    r+=1
  end
  if i==n-1 || (s[i]==">" && s[i+1]=="<")
    cnt+=(l*l-l)/2+(r*r-r)/2+[l,r].max
    l,r=0,0
  end
end
p cnt