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)

# -*- coding: utf-8 -*-

S = input()

ans = 0
stack = 0
height = 0
last_c = '>'
for c in S:
    if last_c == '<' and c == '<':
        stack += 1
    elif last_c == '>' and c == '>':
        stack += 1

    elif last_c == '>' and c == '<':
        # always 0
        ans += stack * (stack - 1) // 2
        ans += max(height, stack)
        stack = 1

    elif last_c == '<' and c == '>':  # < a >
        # bigger
        height = stack
        ans += stack * (stack - 1) // 2
        stack = 1

    last_c = c

if last_c == '<':
    ans += stack * (stack + 1) // 2
else:
    ans += stack * (stack - 1) // 2
    ans += max(height, stack)

print(ans)