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

array = S.scan(/(<+|>+)/).flatten

number = array.map do |a|
  if a[0] == "<" then
    next (0..a.size).to_a
  end

  next a.size.downto(0).to_a
end

i = 0
result = []
while i < number.size do
  n = number[i]
  if i >= 1 && number[i].size <= number[i-1].size then
    n = n[1..-1]
  end

  if i < number.size - 1 && number[i].size <= number[i+1].size then
    n = n[0..-2]
  end
  result << n

  i += 1
end

puts result.flatten.sum