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
N = S.size

nums = Array.new(N + 1, 0)

(0).upto(N - 1) do |idx|
  if S[idx] == '<'
    nums[idx + 1] = [nums[idx + 1], nums[idx] + 1].max
  end
end

(N - 1).downto(0) do |idx|
  if S[idx] == '>'
    nums[idx] = [nums[idx],  nums[idx + 1] + 1].max
  end
end

puts nums.inject(:+)