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 OCaml (4.02.3) (judge verdict: Wrong Answer)

let id x = x

let init n f =
  let rec g i ns = if i = 0 then 0 :: ns else g (i - 1) (i :: ns) in
  List.map f (g n [])

let split_string ?(pattern="") = Str.split @@ Str.regexp pattern

let s = split_string @@ Scanf.scanf "%s\n" id

let f (lst, arr) a =
  match arr with
    | [] -> failwith ""
    | x :: xs -> (a, if a = lst then (x + 1) :: xs else 1 :: x :: xs)

let ss = 
  let t = List.rev_append 
    (if List.hd (List.rev s) = "<" then [0] else [])
    (snd @@ List.fold_left f (List.hd s, [1]) (List.tl s)) in
  if List.hd s = ">" then 0 :: t else t

let rec g = function
  | ([] | _ :: []) -> []
  | x :: y :: xs -> if x > y then x :: (y - 1) :: g xs else (x - 1) :: y :: g xs

let () = 
  ss
    |> g 
    |> List.map (fun i -> i * (i + 1) / 2) 
    |> List.fold_left (+) 0
    |> print_int;
  print_newline ()