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)

s = gets.chomp.chars
a = Array.new(s.size + 1, 0)

cnt = 0
s.chunk{|c| c }.each do |c, items|
  l = items.length
  if c == "<"
    a[cnt] = 0
    1.step(l) do |i|
      a[cnt + i] = a[cnt] + i
    end
  else
    a[cnt + l] = 0
    a[cnt] = [l, a[cnt]].max

    1.step(l) do |i|
      a[cnt + l - i] = [a[cnt + l] + i, a[cnt + l - i]].max
    end
  end
  cnt += l
end

#p s.chunk{|c| c }.map{|c, items| [c, items.length] }
#p a
puts a.inject(:+)
# [0, 3, 2, 1, 0, 1, 2, 0, 1, 2, 3, 4, 5, 2, 1, 0, 1]