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 a = {}
a[#S+1] = 0
for i=#S,1,-1 do
  local c = S:sub(i,i)
  if c == '>' then
    a[i] = a[i+1] + 1
  else
    a[i] = 0
  end
end
for i=1,#S do
  local c = S:sub(i,i)
  if c == '<' and a[i+1] <= a[i] then
    a[i+1] = a[i] + 1
  end
end
local s = 0
for i=1,#a do
  s = s + a[i]
end
print(s)