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: Time Limit Exceeded)

s = list(input())
n = len(s) + 1
a = [0]*n
for i in range(n):
    right = 0
    left = 0
    if i != n-1:
        j = i
        while True:
            if j == n-1 or s[j] != '>':
                break
            right += 1
            j += 1
    if i != 0:
        j = i-1
        while True:
            if j == -1 or s[j] != '<':
                break
            left += 1
            j -= 1
    a[i] = max(right, left)
print(sum(a))