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)

s = input()
ans = 0
prev = None
l = 0
r = 0
for x in s:
  if x == '<':
    if prev == '>':
      mx = max(r, l)
      mn = min(r, l)
      ans += mx * (mx + 1) // 2 + mn * (mn - 1) // 2
      l = 0
      r = 0
    l += 1
  else:
    r += 1
  prev = x
else:
  mx = max(r, l)
  mn = min(r, l)
  ans += mx * (mx + 1) // 2 + mn * (mn - 1) // 2
print(ans)