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 Python (3.4.3) (judge verdict: Wrong Answer)

from itertools import groupby, chain

def pairs(t):
    while True:
        x, y = next(t), next(t)
        a =[sum(1 for _ in g) for k, g in (x, y)]
        yield sum(x * (x - 1) // 2 for x in a) + max(a)

s = input()
t = groupby(s)
d = [(0, ())]
if s[0] == '<':
    t = chain(d, t)
if s[-1] == '>':
    t = chain(t, d)
print(sum(pairs(t)))