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)

import sys
from collections import deque

readline = sys.stdin.readline
readlines = sys.stdin.readlines
ns = lambda: readline().rstrip() # input string
ni = lambda: int(readline().rstrip()) # input int
nm = lambda: map(int, readline().split()) # input multiple int 
nl = lambda: list(map(int, readline().split())) # input multiple int to list

ans = []
s = ns()
n = len(s) + 1
now = 0
min_now = 0

ri = deque()
le = deque()

now = 0
for i in range(n-1):
    if s[i] == '<':
        now += 1
    else:
        now = 0
    le.append(now)
now = 0
for i in range(n-1):
    if s[(n-2)-i] == '>':
        now += 1
    else:
        now = 0
    ri.appendleft(now)
le.appendleft(0)
ri.append(0)

for i in range(n):
    ans.append(max(le[i], ri[i]))

print(sum(ans))