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: Wrong Answer)

s = gets.chomp
cum_up = [0]
cum_down = [0]
tmp = 0

s.each_char do |c|
  c == '<' ? tmp += 1 : tmp = 0
  cum_up << tmp
end

tmp = 0

s.reverse.each_char do |c|
  c == '>' ? tmp += 1 : tmp = 0
  cum_down << tmp
end

size = s.size

puts size.times.map { |i| [cum_down[i], cum_up[size - i]].max }.inject(:+)