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: Runtime Error)

s = gets.chomp
n = s.size

sum = 0
i = 0
a = 0
stack = []
while i < n
  b =
    if s[i] == '<'
      stack << [i, a, sum]
      a + 1
    else
      a - 1
    end
  sum += b
  i += 1
  a = b
  if b < 0
    i = stack_i.pop
    i, a, sum = stack.pop
    b = a + 1 - b
    sum += b
    i += 1
    a = b
  end
end

puts sum