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 (2.7.1) (judge verdict: Accepted)

INCREASE = '<'

s = gets.chomp.split('')
n = s.length + 1
a = Array.new(n, nil)
prev = ''
top_index = nil
s.each_with_index do |t, i|
  if t == prev
    if t == INCREASE
      a[i+1] = a[i]+1
    end
  else
    if t == INCREASE
      a[i] = 0
      a[i+1] = 1
      if top_index
        (top_index..i-1).reverse_each do |j|
          a[j] = a[j+1] + 1
        end
        if top_index > 0
          if a[top_index - 1] == a[top_index]
            a[top_index] = a[top_index] + 1
          elsif a[top_index - 1] > a[top_index]
            a[top_index] = a[top_index-1] + 1
          end
        end
      end
    else
      top_index = i.zero? ? 0 : i
    end
  end
  if i == n - 2 && t != INCREASE
    a[i+1] = 0
    if top_index
      (top_index..i).reverse_each do |j|
        a[j] = a[j+1] + 1
      end
    end
  end
  prev = t
end
puts a.sum