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: Accepted)

import numpy as np
S = list(input())
S_len = len(S)
num_lst = np.zeros(S_len + 1)
for i in range(S_len):
    if S[i] == "<":
        num_lst[i + 1] = max(num_lst[i] + 1, num_lst[i + 1])


for i in range(S_len - 1, -1 , -1):
    if S[i] == ">":
        num_lst[i] = max(num_lst[i], num_lst[i + 1] + 1)
print(int(np.sum(num_lst)))