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 Common Lisp (SBCL 2.0.3) (judge verdict: Accepted)

(let* ((s (read-line))
       (x (make-array (list (length s)) :adjustable t :fill-pointer 0))
       (ans 0))
  (loop :with c := #\=
        :with p := -1
        :for y :across s
        :if (char/= c y)
        :do (progn
              (vector-push-extend 0 x)
              (incf p)
              (setf c y))
        :do (if (char= y #\<)
                (incf (aref x p))
                (decf (aref x p))))
  (loop :for v :across x
        :for w := (abs v)
        :for i :from 0
        :do (incf ans (/ (* w (- w 1)) 2))
        :if (> v 0)
        :do (incf ans (if (= (1+ i) (length x)) w (max w (abs (aref x (1+ i)))))))
  (when (< (aref x 0) 0)
    (incf ans (abs (aref x 0))))
  (format t "~A~%" ans))