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 Lua (5.3.2) (judge verdict: Accepted)

local s = io.read()
local n = #s + 1
local llen, rlen = 0, 0
local toup = true
local lpos = s:sub(1, 1) == ">" and 0 or 1
local turnpos = 0
local sum = 0
if s:sub(n - 1, n - 1) == "<" then
  s = s .. ">"
else
  s = s .. "<"
end
for i = 1, n do
  local ss = s:sub(i, i)
  if ss == "<" then
    if not toup then
      local rlen = i - turnpos
      if llen < rlen then
        sum = sum + llen * (llen - 1) // 2 + rlen * (rlen + 1) // 2
      else
        sum = sum + llen * (llen + 1) // 2 + rlen * (rlen - 1) // 2
      end
      -- print(sum)
      lpos = i
      toup = true
    end
  else
    if toup then
      turnpos = i
      llen = i - lpos
      toup = false
    end
  end
end
if not toup then
  local rlen = n - turnpos
  -- print(rlen)
  if llen < rlen then
    sum = sum + llen * (llen - 1) // 2 + rlen * (rlen + 1) // 2
  else
    sum = sum + llen * (llen + 1) // 2 + rlen * (rlen - 1) // 2
  end
end
print(sum)