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.split('')

n = Array.new(s.size + 1, nil)

n.size.times do |i|
  if i == 0
    if s[i] == '<'
      n[i] = 0
    else
      n[i] = n[i+1] + 1 if n[i+1]
    end
  elsif i == n.size-1
    if s[i-1] == '<'
      n[i] = n[i-1] + 1 if n[i-1]
    else
      n[i] = 0
    end
  else
    if s[i-1] == '<'
      if s[i] == '<'
        n[i] = n[i-1] + 1 if n[i-1]
      else
        n[i] = [n[i-1], n[i+1]].max + 1 if n[i-1] && n[i+1]
      end
    else
      if s[i] == '>'
        n[i] = n[i+1] + 1 if n[i+1]
      else
        n[i] = 0
      end
    end
  end
end

(n.size - 1).downto(0) do |i|
  if i == 0
    if s[i] == '<'
      n[i] = 0
    else
      n[i] = n[i+1] + 1 if n[i+1]
    end
  elsif i == n.size-1
    if s[i-1] == '<'
      n[i] = n[i-1] + 1 if n[i-1]
    else
      n[i] = 0
    end
  else
    if s[i-1] == '<'
      if s[i] == '<'
        n[i] = n[i-1] + 1 if n[i-1]
      else
        n[i] = [n[i-1], n[i+1]].max + 1 if n[i-1] && n[i+1]
      end
    else
      if s[i] == '>'
        n[i] = n[i+1] + 1 if n[i+1]
      else
        n[i] = 0
      end
    end
  end
end

p n.inject(:+)