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: Accepted)

import qualified Data.Text as T
import qualified Data.Text.IO as T
import qualified Data.Text.Read as T
import Data.List (group)
import Data.Bits (shiftR)

main :: IO ()
main = do
  s <- getLine :: IO String
  let
    r :: Int
    r = sum . map h . g Nothing . map f . group $ s
      where
        f :: String -> (Bool, Int)
        f = (,) <$> (== '<') . head <*> length
        g :: Maybe Int -> [(Bool, Int)] -> [(Int, Int)]
        g Nothing ((True, l) : ps) = g (Just l) ps
        g (Just l) ((False, l') : ps) = (l, l') : g Nothing ps
        g _ ((_, l') : ps) = (0, l') : g Nothing ps
        g (Just l) _ = [(l, 0)]
        g _ _ = []
        h :: (Int, Int) -> Int
        h (l, l') = shiftR (l * pred l) 1 + shiftR (l' * pred l') 1 + max l l'
  print r

unsafeSignedDecimal :: T.Text -> Int
unsafeSignedDecimal s = case T.signed T.decimal s of
  Right (n, _) -> n