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)

arr = gets.chomp.split('')
prev = arr[0]
index = 0
list = []
(1..arr.count).each do |i|
  if i < arr.count
    if prev + arr[i] == '><'
      list << arr.slice(index...i)
      index = i
    end
    prev = arr[i]
  else
    list << arr.slice(index...i)
  end
end
sum = 0
list.each do |i|
  l = i.count('<')
  r = i.count - l
  sum += (l + 1) * l / 2
  sum += (r + 1) * r / 2
  sum -= [l, r].min
end
puts sum