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)

import math

S = input()
pad = []
left_flag = S[0] == "<"
count = 0
for k in S:
    if left_flag and k == "<":
        count += 1
    elif left_flag and k == ">":
        pad.append(count)
        left_flag ^= 1
        count = 1
    elif (not left_flag) and k == ">":
        count += 1
    else:
        pad.append(-count)
        left_flag ^= 1
        count = 1
if left_flag:
    pad.append(count)
else:
    pad.append(-count)


result = 0
for i, j in zip(pad[0::2], pad[1::2]):
    if i > abs(j):
        result += sum(range(i + 1)) + sum(range(abs(j)))
    else:
        result += sum(range(i)) + sum(range(abs(j) + 1))
if len(pad) % 2 == 1:
    result += sum(range(pad[-1]))
print(result)