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: Time Limit Exceeded)

import qualified Data.ByteString.Char8 as BS

readString = map BS.unpack . BS.words

getString = readString <$> BS.getLine

calc :: String -> Int
calc [] = 0
calc ss = k + calc ss''
  where
    len_ss = length ss
    ss' = dropWhile (== '<') ss
    len_ss' = len_ss - length ss'
    ss'' = dropWhile (== '>') ss'
    len_ss'' = length ss' - length ss''
    k = len_ss' `seq` len_ss'' `seq` sum [0 .. maximum [len_ss' - 1, 0]] + sum [0 .. maximum [len_ss'' - 1, 0]] + maximum [len_ss', len_ss'']

main = do
  [s] <- getString
  print $ calc s