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)

S = gets.chomp
a = []
m = 0
n = 0
answer = 0
if S[0] == ">"
    a.push(0)
end
for i in 0...S.size do
    if S[i] == "<"
        if n > 0
            a.push(n)
            n = 0
        end
        m += 1
    else
        if m > 0
            a.push(m)
            m = 0
        end
        n += 1
    end
end
if S[-1] == "<"
    a.push(m)
    a.push(0)
else
    a.push(n)
end
for i in 0...a.size/2 do
    j = 2*i
    x = a[j]
    y = a[j+1]
    answer += x*(x+1)/2
    answer += y*(y+1)/2
    if x > y
        answer -= y
    else
        answer -= x
    end
end
puts answer