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: Runtime Error)

S = gets.chomp.chars.slice_when{|a,b| a != b}.to_a.map{|v|[v[0], v.size]}

def acc(n)
  n*(n+1)/2
end

count = 0

if S[0][0] == ">"
  s = s.shift
  count += acc(s[1])
end

S.each_slice(2) do |a,b|
  if b.nil?
    count += acc(a[1])
    break
  end

  if a[1] < b[1]
    count += acc(a[1]-1)
    count += acc(b[1])
  else
    count += acc(a[1])
    count += acc(b[1]-1)
  end
end

puts count