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: Runtime Error)

import re
S = input()

po=[]
ne=[]
li = [m.span()[0] for m in re.finditer('><', S)]
result = []

n = 0
for i in S:
    if i == "<":
        n += 1
    else:
        po.append(n)
        break
for i in li:
    s = "<"
    n = 0
    while s == S[i+1]:
        n += 1
        i += 1
        if i+1 >= len(S):
            break
    po.append(n)
for i in li:
    s = ">"
    n = 0
    while s == S[i]:
        n += 1
        i -= 1
    ne.append(n)
n = 0
for i in S[::-1]:
    if i == ">":
        n += 1
    else:
        ne.append(n)
        break
if len(po) == 0:
    result.append((1/2)*ne[i]*(ne[i]+1))
if len(ne) == 0:
    result.append((1/2)*po[i]*(po[i]+1))
for i,l in enumerate(po):
    if l < ne[i]:
        if l > 0:
            result.append((1/2)*(l-1)*l)
        if ne[i] > 0:
            result.append((1/2)*ne[i]*(ne[i]+1))
    else:
        if l > 0:
            result.append((1/2)*l*(l+1))
        if ne[i] > 0:
            result.append((1/2)*ne[i]*(ne[i]-1))
print(int(sum(result)))