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 1.1.14) (judge verdict: Wrong Answer)

(defun f(s)
  (labels ((rec(i lastc n acc)
             (format t "~A ~A ~A ~A~%" i lastc n acc)
             (if (= i (length s))
               (+ (/ (* n (1+ n)) 2) acc)
               (if (char= (char s i) lastc)
                 (rec (1+ i) lastc (1+ n) acc)
                 (if (= n 1)
                   (if (char= (char s i) #\>)
                     (rec (1+ i) (char s i) 1 acc)
                     (rec (1+ i) (char s i) 1 (1+ acc)))
                   (if (char= (char s i) #\<)
                     (rec (1+ i) (char s i) 1 (+ acc (/ (* n (1+ n)) 2)))
                     (rec (1+ i) (char s i) 0 (+ acc (/ (* n (1+ n)) 2)))
                     ))))))
    (rec 1 (char s 0) 1 0)))
(let ((line (read-line nil nil)))
  (format t "~A~%" (f line)))