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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.List

main :: IO ()
main = do
  l1 <- getLine
  let s1 = l1
  print $ f s1 0

f [] n = 0
f "<" n = n + n + 1
f ">" n = n
f ('<':s) n = n + f s (n+1)
f s@('>':_) n = g (m - 1) + (max n m) + f s' 0
  where (l, s') = span (=='>') s
        m = length l

g n = (n*(n+1))`div`2