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 Ruby (2.3.3) (judge verdict: Accepted)

# N = gets.chomp.to_i
# A, B, C = gets.chomp.split.map(&:to_i)
S = gets.chomp.chars
N = S.size + 1

# We use queue
DP = Array.new(N, -1)  # A

if S[0] == '<'
  DP[0] = 0
end
if S[N-2] == '>'
  DP[N-1] = 0
end

1.upto(N-2).each do |i|
  if (S[i-1] == '>' && S[i] == '<')
    DP[i] = 0
  end
end

# Set number from left
1.upto(N-2).each do |i|
  next if DP[i-1] == -1

  if (S[i-1] == '<' && S[i] == '<')
    DP[i] = DP[i-1] + 1
  end
end

# Set number from right
(N-2).downto(1).each do |i|
  next if DP[i+1] == -1

  if (S[i-1] == '>' && S[i] == '>')
    DP[i] = DP[i+1] + 1
  end
end

if S[0] == '>'
  DP[0] = DP[1] + 1
end
if S[N-2] == '<'
  DP[N-1] = DP[N-2]+1
end

# Set < >
1.upto(N-2).each do |i|
  if (S[i-1] == '<' && S[i] == '>')
    DP[i] = [DP[i-1], DP[i+1]].max + 1
  end
end

# For Debug
# p DP

ans = 0
0.upto(N-1).each do |i|
  ans += DP[i]
end

p ans