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: Time Limit Exceeded)

import sys

inp = sys.stdin.readline()[:-1]
N = len(inp) - 1

from_left = []
from_right = []
less_row = 0
more_row = 0
for i, c in enumerate(inp):
    if c == "<":
        less_row += 1
    else:
        if less_row:
            from_left.append((less_row, less_row * (less_row + 1) // 2))
        less_row = 0

    r_i = N - i
    if inp[r_i] == ">":
        more_row += 1
    else:
        if more_row:
            from_right.insert(0, (more_row, more_row * (more_row + 1) // 2))
        more_row = 0

if less_row:
    from_left.append((less_row, less_row * (less_row + 1) // 2))
if more_row:
    from_right.insert(0, (more_row, more_row * (more_row + 1) // 2))

ans = 0
if inp[-1] == "<":
    ans += from_left.pop()[1]
if inp[0] == ">":
    ans += from_right.pop(0)[1]


def big_boy(it):
    r_last, r_tri = from_right[it[0]]
    return it[1][1] + r_tri - min(it[1][0], r_last)


print(ans + sum(map(big_boy, enumerate(from_left))))