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.chars

nums = Array.new(S.size + 1, -1)

chain = 0

S.each_with_index do |s, idx|
  if s == '<'
    nums[idx] = chain
    nums[idx + 1] = chain + 1
    chain += 1
  else
    chain = 0
  end
end

# p nums
N = S.size
chain = 0

S.reverse.each_with_index do |s, idx|
  if s == '>'
    nums[N - idx] = chain
    nums[N - idx - 1] = [nums[N - idx - 1],  chain + 1].max
    chain += 1
  else
    if S[N - idx - 1] == '>' && nums[N - idx - 1] >= chain
      # nums[N - idx] = chain + 1
    end

    chain = 0
  end
end

# p nums
puts nums.inject(:+)