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)

def sums(n)
  return n*(n+1)/2
end

s = gets.chomp.split("")
cmps = Array.new(0)
mark = Array.new(0)

cnt = 1
pre = s[0]
for i in 1..(s.length-1)
  if s[i] == pre
    cnt += 1
  else
    cmps.push(cnt)
    mark.push(pre)
    cnt = 1
  end
  pre = s[i]
end
cmps.push(cnt)
mark.push(pre)

ans = 0
for i in 0..(cmps.length-1)
  if i == 0
    if cmps.length == 1 || mark[i] == ">"
      ans += sums(cmps[i])
    else
      ans += sums(cmps[i]-1)
    end
  else
    if mark[i] == "<"
      ans += sums(cmps[i])
    elsif mark[i] == ">"
      if cmps[i-1] < cmps[i]
        ans += sums(cmps[i])
      else
        ans += sums(cmps[i]-1)
      end
    end
  end
end
puts ans