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)

S = input()
def rle_encode(data):
    encoding = []
    prev_char = ''
    count = 1

    if not data: return ''

    for char in data:
        # If the prev and current characters
        # don't match...
        if char != prev_char:
            # ...then add the count and character
            # to our encoding
            if prev_char:
                encoding.append([int(count), prev_char])
            count = 1
            prev_char = char
        else:
            # Or increment our counter
            # if the characters do match
            count += 1
    else:
        # Finish off the encoding
        encoding.append([int(count), prev_char])
        return encoding

S_rle = list(rle_encode(S))
total = 0
if S_rle[0][1] == '>':
  head = S_rle[0]
  S_rle.pop(0)
  total += sum(range(head[0]))
else:
  head = []
if S_rle[-1][1] == '<':
  tail = S_rle[-1]
  S_rle.pop(-1)
  total += sum(range(tail[0]))
else:
  tail = []
body = S_rle[:]
for i in range(len(body)//2):
  num1, num2 = body[2*i][0], body[2*i+1][0]
  total += sum(range(max(num1, num2)+1)) + sum(range(min(num1, num2)))
print(total)