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 (2.7.1) (judge verdict: Wrong Answer)

s = gets.chomp
len = s.length
ans = []
cnt = 0
num = 0
if s[0] == "<"
  ans << num
else
  cnt += 1
end
(len-1).times do |i|
  if s[i] == "<" && s[i+1] == "<"
    num += 1
    ans << num
  elsif s[i] == "<" && s[i+1] == ">"
    num += 1
  elsif s[i] == ">" && s[i+1] == "<"
    cnt += 1
    cnt.times do |j|
      if j == 0 && num > cnt-j
        ans << num
      else
        ans << cnt-j
      end
    end
    cnt = 0
    num = 0
    ans << num
  elsif s[i] == ">" && s[i+1] == ">"
    cnt += 1
  end
end
if s[-1] == ">"
  cnt.times do |j|
    if j == 0 && num > cnt-j
      ans << num
    else
      ans << cnt-j
    end
  end
  ans << 0
else
  num += 1
  cnt += 1
  cnt.times do |j|
    if j == 0 && num > cnt-j
      ans << num
    else
      ans << cnt-j
    end
  end
end
puts ans.inject(:+)